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Approximation and entropy numbers of Volterra operators with application to Brownian motion / / Mikhail A. Lifshits, Werner Linde
| Approximation and entropy numbers of Volterra operators with application to Brownian motion / / Mikhail A. Lifshits, Werner Linde |
| Autore | Lifshit͡s M. A (Mikhail Anatolʹevich), <1956-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2002 |
| Descrizione fisica | 1 online resource (103 p.) |
| Disciplina |
510 s
515/.723 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Volterra operators
Entropy (Information theory) Brownian motion processes |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0338-2 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Main Results""; ""Chapter 3. Scale Transformations""; ""3.1. Increasing Transformations ""; ""3.2. Decreasing Transformations ""; ""3.3. Examples ""; ""3.4. Transformations and Norms ""; ""Chapter 4. Upper Estimates for Entropy Numbers""; ""4.1. A General Bound Based on Partitions""; ""4.2. Proof of Theorem 2.2 (1)""; ""4.3. Proof of Parts (2) and (3) in Theorem 2.2""; ""4.4. Entropy Estimates for T[sub(p,Î?)]""; ""4.5. Proof of Theorem 2.3""; ""4.6. Upper Bounds for Forward Integration Operators""; ""4.7. Proof of Theorem 4.9""
""7.1. Gaussian Processes and Metric Entropy""""7.2. Weighted Wiener Processes""; ""7.3. Small Ball Estimates for Wiener Processes""; ""7.4. Exact Small Ball Estimates""; ""Appendix""; ""Bibliography"" |
| Record Nr. | UNINA-9910480221903321 |
Lifshit͡s M. A (Mikhail Anatolʹevich), <1956->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Approximation and entropy numbers of Volterra operators with application to Brownian motion / / Mikhail A. Lifshits, Werner Linde
| Approximation and entropy numbers of Volterra operators with application to Brownian motion / / Mikhail A. Lifshits, Werner Linde |
| Autore | Lifshit͡s M. A (Mikhail Anatolʹevich), <1956-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2002 |
| Descrizione fisica | 1 online resource (103 p.) |
| Disciplina |
510 s
515/.723 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Volterra operators
Entropy (Information theory) Brownian motion processes |
| ISBN | 1-4704-0338-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Main Results""; ""Chapter 3. Scale Transformations""; ""3.1. Increasing Transformations ""; ""3.2. Decreasing Transformations ""; ""3.3. Examples ""; ""3.4. Transformations and Norms ""; ""Chapter 4. Upper Estimates for Entropy Numbers""; ""4.1. A General Bound Based on Partitions""; ""4.2. Proof of Theorem 2.2 (1)""; ""4.3. Proof of Parts (2) and (3) in Theorem 2.2""; ""4.4. Entropy Estimates for T[sub(p,Î?)]""; ""4.5. Proof of Theorem 2.3""; ""4.6. Upper Bounds for Forward Integration Operators""; ""4.7. Proof of Theorem 4.9""
""7.1. Gaussian Processes and Metric Entropy""""7.2. Weighted Wiener Processes""; ""7.3. Small Ball Estimates for Wiener Processes""; ""7.4. Exact Small Ball Estimates""; ""Appendix""; ""Bibliography"" |
| Record Nr. | UNINA-9910788846403321 |
|
Lifshit͡s M. A (Mikhail Anatolʹevich), <1956->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Approximation and entropy numbers of Volterra operators with application to Brownian motion / / Mikhail A. Lifshits, Werner Linde
| Approximation and entropy numbers of Volterra operators with application to Brownian motion / / Mikhail A. Lifshits, Werner Linde |
| Autore | Lifshit͡s M. A (Mikhail Anatolʹevich), <1956-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2002 |
| Descrizione fisica | 1 online resource (103 p.) |
| Disciplina |
510 s
515/.723 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Volterra operators
Entropy (Information theory) Brownian motion processes |
| ISBN | 1-4704-0338-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Main Results""; ""Chapter 3. Scale Transformations""; ""3.1. Increasing Transformations ""; ""3.2. Decreasing Transformations ""; ""3.3. Examples ""; ""3.4. Transformations and Norms ""; ""Chapter 4. Upper Estimates for Entropy Numbers""; ""4.1. A General Bound Based on Partitions""; ""4.2. Proof of Theorem 2.2 (1)""; ""4.3. Proof of Parts (2) and (3) in Theorem 2.2""; ""4.4. Entropy Estimates for T[sub(p,Î?)]""; ""4.5. Proof of Theorem 2.3""; ""4.6. Upper Bounds for Forward Integration Operators""; ""4.7. Proof of Theorem 4.9""
""7.1. Gaussian Processes and Metric Entropy""""7.2. Weighted Wiener Processes""; ""7.3. Small Ball Estimates for Wiener Processes""; ""7.4. Exact Small Ball Estimates""; ""Appendix""; ""Bibliography"" |
| Record Nr. | UNINA-9910818013603321 |
|
Lifshit͡s M. A (Mikhail Anatolʹevich), <1956->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2002 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Asymptotics and Mellin-Barnes integrals / / R.B. Paris, D. Kaminski [[electronic resource]]
| Asymptotics and Mellin-Barnes integrals / / R.B. Paris, D. Kaminski [[electronic resource]] |
| Autore | Paris R. B. |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2001 |
| Descrizione fisica | 1 online resource (xvi, 422 pages) : digital, PDF file(s) |
| Disciplina | 515/.723 |
| Collana | Encyclopedia of mathematics and its applications |
| Soggetto topico |
Mellin transform
Asymptotic expansions |
| ISBN |
1-107-12112-4
1-280-41805-2 9786610418053 1-139-14661-0 0-511-17409-8 0-511-06706-2 0-511-06075-0 0-511-32800-1 0-511-54666-1 0-511-06919-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Order Relations -- Asymptotic Expansions -- Other Expansions -- Biographies of Mellin and Barnes -- Fundamental Results -- The Gamma Function [Gamma] (z) -- The Asymptotic Expansion of [Gamma] (z) -- The Stirling Coefficients -- Bounds for [Gamma] (z) -- Expansion of Quotients of Gamma Functions -- Inverse Factorial Expansions -- A Recursion Formula when [alpha subscript r] = [beta subscript r] -- An Algebraic Method for the Determination of the A[subscript j] -- Special Cases -- The Asymptotic Expansion of Integral Functions -- Convergence of Mellin-Barnes Integrals -- Order Estimates for Remainder Integrals -- Lemmas -- Properties of Mellin Transforms -- Basic Properties -- Translational and Differential Properties -- The Parseval Formula -- Analytic Properties -- Inverse Mellin Transforms -- Integrals Connected with e[superscript -z] -- Some Standard Integrals -- Discontinuous Integrals -- Gamma-Function Integrals -- Ramanujan-Type Integrals -- Barnes' Lemmas -- Mellin-Barnes Integral Representations -- The Confluent Hypergeometric Functions -- The Gauss Hypergeometric Function -- Some Special Functions -- Applications of Mellin Transforms -- Transformation of Series -- The Mellin Transform Method -- The Poisson-Jacobi Formula -- An Infinite Series -- A Smoothed Dirichlet Series -- A Finite Sum -- Number-Theoretic Examples -- A Harmonic Sum -- Euler's Product -- Ramanujan's Function -- Some Other Number-Theoretic Sums -- Solution of Differential Equations -- Potential Problems in Wedge-Shaped Regions. |
| Altri titoli varianti | Asymptotics & Mellin-Barnes Integrals |
| Record Nr. | UNINA-9910450367603321 |
|
Paris R. B.
|
||
| Cambridge : , : Cambridge University Press, , 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Asymptotics and Mellin-Barnes integrals / / R.B. Paris, D. Kaminski [[electronic resource]]
| Asymptotics and Mellin-Barnes integrals / / R.B. Paris, D. Kaminski [[electronic resource]] |
| Autore | Paris R. B. |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2001 |
| Descrizione fisica | 1 online resource (xvi, 422 pages) : digital, PDF file(s) |
| Disciplina | 515/.723 |
| Collana | Encyclopedia of mathematics and its applications |
| Soggetto topico |
Mellin transform
Asymptotic expansions |
| ISBN |
1-107-12112-4
1-280-41805-2 9786610418053 1-139-14661-0 0-511-17409-8 0-511-06706-2 0-511-06075-0 0-511-32800-1 0-511-54666-1 0-511-06919-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Order Relations -- Asymptotic Expansions -- Other Expansions -- Biographies of Mellin and Barnes -- Fundamental Results -- The Gamma Function [Gamma] (z) -- The Asymptotic Expansion of [Gamma] (z) -- The Stirling Coefficients -- Bounds for [Gamma] (z) -- Expansion of Quotients of Gamma Functions -- Inverse Factorial Expansions -- A Recursion Formula when [alpha subscript r] = [beta subscript r] -- An Algebraic Method for the Determination of the A[subscript j] -- Special Cases -- The Asymptotic Expansion of Integral Functions -- Convergence of Mellin-Barnes Integrals -- Order Estimates for Remainder Integrals -- Lemmas -- Properties of Mellin Transforms -- Basic Properties -- Translational and Differential Properties -- The Parseval Formula -- Analytic Properties -- Inverse Mellin Transforms -- Integrals Connected with e[superscript -z] -- Some Standard Integrals -- Discontinuous Integrals -- Gamma-Function Integrals -- Ramanujan-Type Integrals -- Barnes' Lemmas -- Mellin-Barnes Integral Representations -- The Confluent Hypergeometric Functions -- The Gauss Hypergeometric Function -- Some Special Functions -- Applications of Mellin Transforms -- Transformation of Series -- The Mellin Transform Method -- The Poisson-Jacobi Formula -- An Infinite Series -- A Smoothed Dirichlet Series -- A Finite Sum -- Number-Theoretic Examples -- A Harmonic Sum -- Euler's Product -- Ramanujan's Function -- Some Other Number-Theoretic Sums -- Solution of Differential Equations -- Potential Problems in Wedge-Shaped Regions. |
| Altri titoli varianti | Asymptotics & Mellin-Barnes Integrals |
| Record Nr. | UNINA-9910783125203321 |
|
Paris R. B.
|
||
| Cambridge : , : Cambridge University Press, , 2001 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz
| Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz |
| Autore | Katz Nicholas M. <1943-> |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton ; ; Oxford, : Princeton University Press, c2012 |
| Descrizione fisica | 1 online resource (213 p.) |
| Disciplina | 515/.723 |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Mellin transform
Convolutions (Mathematics) Sequences (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-37996-1
9786613379962 1-4008-4270-0 |
| Classificazione | SI 830 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Introduction -- CHAPTER 1. Overview -- CHAPTER 2. Convolution of Perverse Sheaves -- CHAPTER 3. Fibre Functors -- CHAPTER 4. The Situation over a Finite Field -- CHAPTER 5. Frobenius Conjugacy Classes -- CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith -- CHAPTER 7. The Main Theorem -- CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility -- CHAPTER 9. Autodualities and Signs -- CHAPTER 10. A First Construction of Autodual Objects -- CHAPTER 11. A Second Construction of Autodual Objects -- CHAPTER 12. The Previous Construction in the Nonsplit Case -- CHAPTER 13. Results of Goursat-Kolchin-Ribet Type -- CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick -- CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family -- CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith -- CHAPTER 17. GL(n) Examples -- CHAPTER 18. Symplectic Examples -- CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples -- CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples -- CHAPTER 21. SL(n) Examples, for n an Odd Prime -- CHAPTER 22. SL(n) Examples with Slightly Composite n -- CHAPTER 23. Other SL(n) Examples -- CHAPTER 24. An O(2n) Example -- CHAPTER 25. G2 Examples: the Overall Strategy -- CHAPTER 26. G2 Examples: Construction in Characteristic Two -- CHAPTER 27. G2 Examples: Construction in Odd Characteristic -- CHAPTER 28. The Situation over ℤ: Results -- CHAPTER 29. The Situation over ℤ: Questions -- CHAPTER 30. Appendix: Deligne's Fibre Functor -- Bibliography -- Index |
| Record Nr. | UNINA-9910461830703321 |
|
Katz Nicholas M. <1943->
|
||
| Princeton ; ; Oxford, : Princeton University Press, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz
| Convolution and equidistribution [[electronic resource] ] : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz |
| Autore | Katz Nicholas M. <1943-> |
| Edizione | [Course Book] |
| Pubbl/distr/stampa | Princeton ; ; Oxford, : Princeton University Press, c2012 |
| Descrizione fisica | 1 online resource (213 p.) |
| Disciplina | 515/.723 |
| Collana | Annals of mathematics studies |
| Soggetto topico |
Mellin transform
Convolutions (Mathematics) Sequences (Mathematics) |
| Soggetto non controllato |
ArtinГchreier reduced polynomial
Emanuel Kowalski EulerАoincar formula Frobenius conjugacy class Frobenius conjugacy Frobenius tori GoursatЋolchinВibet theorem Kloosterman sheaf Laurent polynomial Legendre Mellin transform Pierre Deligne Ron Evans Tannakian category Tannakian groups Zeeev Rudnick algebro-geometric autodual objects autoduality characteristic two connectedness dimensional objects duality equidistribution exponential sums fiber functor finite field Mellin transform finite field finite fields geometrical irreducibility group scheme hypergeometric sheaf interger monic polynomials isogenies lie-irreducibility lisse middle convolution middle extension sheaf monic polynomial monodromy groups noetherian connected scheme nonsplit form nontrivial additive character number theory odd characteristic odd prime orthogonal case perverse sheaves polynomials pure weight semisimple object semisimple sheaves signs split form supermorse theorem theorems |
| ISBN |
1-283-37996-1
9786613379962 1-4008-4270-0 |
| Classificazione | SI 830 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Front matter -- Contents -- Introduction -- CHAPTER 1. Overview -- CHAPTER 2. Convolution of Perverse Sheaves -- CHAPTER 3. Fibre Functors -- CHAPTER 4. The Situation over a Finite Field -- CHAPTER 5. Frobenius Conjugacy Classes -- CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith -- CHAPTER 7. The Main Theorem -- CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility -- CHAPTER 9. Autodualities and Signs -- CHAPTER 10. A First Construction of Autodual Objects -- CHAPTER 11. A Second Construction of Autodual Objects -- CHAPTER 12. The Previous Construction in the Nonsplit Case -- CHAPTER 13. Results of Goursat-Kolchin-Ribet Type -- CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick -- CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family -- CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith -- CHAPTER 17. GL(n) Examples -- CHAPTER 18. Symplectic Examples -- CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples -- CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples -- CHAPTER 21. SL(n) Examples, for n an Odd Prime -- CHAPTER 22. SL(n) Examples with Slightly Composite n -- CHAPTER 23. Other SL(n) Examples -- CHAPTER 24. An O(2n) Example -- CHAPTER 25. G2 Examples: the Overall Strategy -- CHAPTER 26. G2 Examples: Construction in Characteristic Two -- CHAPTER 27. G2 Examples: Construction in Odd Characteristic -- CHAPTER 28. The Situation over ℤ: Results -- CHAPTER 29. The Situation over ℤ: Questions -- CHAPTER 30. Appendix: Deligne's Fibre Functor -- Bibliography -- Index |
| Record Nr. | UNINA-9910789730903321 |
|
Katz Nicholas M. <1943->
|
||
| Princeton ; ; Oxford, : Princeton University Press, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Discrete Taylor Transform and Inverse Transform
| Discrete Taylor Transform and Inverse Transform |
| Autore | Baghai-Wadji Alireza |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Newark : , : John Wiley & Sons, Incorporated, , 2024 |
| Descrizione fisica | 1 online resource (0 pages) |
| Disciplina | 515/.723 |
| Soggetto topico | Integral transforms |
| ISBN |
9781394240081
1394240082 9781394240098 1394240090 9781394240104 1394240104 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Cover -- Title Page -- Copyright -- Contents -- About the Author -- Preface -- Introduction -- I.1 Notation and Elementary Notions -- I.2 Orthonormal Bases and Their Corresponding Dual Bases -- I.3 Fourier Transform and Inverse Transform and the AssociatedResolution of Identity -- Chapter 1 Toy Model I‐1: {−Δ,0,Δ} -- 1.1 Introduction -- 1.1.1 Symmetric Equidistant Sampling -- 1.1.2 Difference Operators -- 1.2 Frames and Dual Frames Induced by the Monomials 1, x, and x2 -- 1.2.1 Brief Summary of the Essentials -- 1.2.2 Frame Vectors -- 1.2.3 Frame Operator -- 1.2.4 Inverse Frame Operator -- 1.2.5 Dual‐Frame Vectors -- 1.2.6 Dual‐Frame Operator -- 1.2.7 The Resolution of the Identity -- 1.2.8 D‐TTIT in 3D -- Chapter 2 Toy Model I‐2:{0,Δ,2Δ} -- 2.1 Introduction -- 2.1.1 Difference Operators -- 2.2 Frames and Dual Frames Induced by Monomials 1, x, and x2 -- 2.2.1 Frame Vectors -- 2.2.2 Frame Operator -- 2.2.3 Inverse Frame Operator -- 2.2.4 Dual‐Frame Vectors -- 2.2.5 Dual‐Frame Operator -- 2.2.6 The Resolution of the Identity -- 2.2.7 D‐TTIT in 3‐D -- Chapter 3 Toy Model I‐3: {−2Δ,−Δ,0} -- 3.1 Introduction -- 3.1.1 Difference Operators -- 3.2 Frames and Dual Frames -- 3.2.1 Frame Vectors -- 3.2.2 Frame Operator -- 3.2.3 Inverse Frame Operator -- 3.2.4 Dual‐Frame Vectors -- 3.2.5 The Resolution of the Identity -- 3.2.6 D‐TTIT in 3‐D -- Chapter 4 Toy Model I‐4: {−Δ,0,Δ} -- 4.1 Overcompleteness -- 4.1.1 Difference Operators -- 4.2 Frames and Dual Frames -- 4.2.1 Frame Vectors -- 4.2.2 Frame Operator -- 4.2.3 Inverse Frame Operator -- 4.2.4 Dual Frame Vectors -- 4.2.5 The Resolution of the Identity -- 4.2.6 Establishing Relationships Between the Dual Frame Vectors |1˜> -- , |x˜> -- , |x˜2> -- , |x˜3> -- , and |x˜4> -- , and the Difference Operators |D(0)> -- , |D(1)> -- , and |D(2)>.
4.2.7 Establishing Relationships Between the Dual Frame Vectors |1˜> -- , |x˜> -- , |x˜2> -- , |x˜3> -- , |x˜4> -- , |x˜5> -- , and |x˜6> -- , and the Difference Operators |D(0)> -- , |D(1)> -- , and |D(2)> -- -- Chapter 5 Toy Model I‐5: {−2Δ, −Δ, 0, Δ, 2Δ} -- 5.1 Introduction -- 5.2 Difference Operators -- 5.3 Frames and Dual Frames -- 5.3.1 Dual‐Frame Vectors -- 5.3.1.1 On the Construction of |1˜> -- -- 5.3.1.2 On the Construction of |x˜> -- -- 5.3.1.3 On the Construction of |x˜2> -- -- 5.3.1.4 On the Construction of |x˜3> -- -- 5.3.1.5 On the Construction of |x˜4> -- -- 5.3.2 Dual‐Frame Operator -- Chapter 6 Toy Model I‐7: {−3Δ,−2Δ,−Δ,0,Δ,2Δ,3Δ} -- 6.1 Introduction -- 6.2 Difference Operators -- 6.3 Frame Vectors -- 6.4 Frame Operator -- 6.5 Inverse Frame Operator -- 6.6 Constructing Skeleton Matrices for S7×7−1 -- 6.7 Practical Implementation -- 6.8 Dual Vectors -- 6.8.1 Summarizing the Results Obtained -- 6.9 Dual‐Frame Operator -- 6.10 Conclusions -- Chapter 7 Self‐consistent Expressions for |D(n)> -- -- 7.1 The Interval [−Δ,Δ] -- 7.2 The Interval [−2Δ,2Δ] -- 7.3 The Interval [−3Δ,3Δ] -- Chapter 8 Toy Model I‐3: {Δ−1,Δ0,Δ1} -- 8.1 A Guide Through the Chapter -- 8.2 Univariate Functions on Three Nonuniformly Distributed Lattice Points: Derivatives at an Inner Cluster Point -- 8.3 Setting Up the System of Equations for the Determination of Df(n) (n& -- equals -- 0,1,2) -- 8.4 Matrix Multiplication Expressed in Terms of Exterior Products -- 8.4.1 General Considerations -- 8.4.2 The Resolution of Identity -- 8.4.3 The Frame Operator -- 8.4.4 Preliminary Summary -- 8.5 Solving the System of Equations in (8.7) by Successive Elimination (Method 1) -- 8.5.1 Obtaining the Expressions of the Universal Derivative Kets |D(n)> -- Defined by Df(n)& -- equals -- < -- D(n)|F> -- (n& -- equals -- 0,1,2). 8.6 Exterior Products |xn> -- < -- D(n)| (n& -- equals -- 0,1,2) and the Resolution of Identity (Property 1) -- 8.7 Inner Products < -- xn|D(n)> -- & -- equals -- δmn (m,n& -- equals -- 0,1,2) (Property 2) -- 8.8 Calculation of the Derivative Operators Based on the Inverse of the Δ‐Matrix (Method 2) -- 8.9 Calculating the Derivative Operators Based on the Frame Operator (Method 3) -- 8.9.1 The Exterior Product of the Kets |xn> -- with Their Bra Counterpart < -- xn| -- 8.9.2 The Exterior Product of the Ket |1> -- with Its Bra Counterpart -- 8.9.3 The Exterior Product of the Ket |x> -- with Its Bra Counterpart -- 8.9.4 The Exterior Product of the Ket |x2> -- with Its Bra Counterpart -- 8.9.5 The S‐Matrix and Its Properties -- 8.9.6 Calculation of < -- D(0)| Utilizing S−1 and the Position Bra < -- x(0)| -- 8.9.7 Calculation of < -- D(1)| Utilizing S−1 and the Position Bra < -- x(1)| -- 8.9.8 Calculation of < -- D(2)| Utilizing S−1 and the Position Bra < -- x(2)| -- 8.10 Construction of the Derivative Operators in Terms of Rational Polynomials (Method 4) -- 8.11 Construction of the Derivative Operators Simply‐by‐Inspection of Indices (Method 5) -- 8.12 Uniform Lattices -- 8.12.1 Properties of the Derivative Operators on Uniform Lattices -- 8.12.2 Relating < -- D(n)| to f(n)(0) (n& -- equals -- 0,1,2) -- 8.13 Conclusions -- Chapter 9 Toy Model I‐5: {Δ−2,Δ−1,Δ0,Δ1,Δ2} -- 9.1 The Resolution of Identity -- 9.2 Setting Up the System of Equations -- 9.3 Solving the System of Equation in (9.18) by Successive Elimination -- 9.4 Obtaining the Expressions of the Universal Difference Operators |D(n)> -- Defined by Df(n)& -- equals -- < -- D(n)|F> -- -- 9.5 Simplifying the Expressions of the Difference Operators -- 9.6 Exterior Products of the Position Kets and their Dual Difference Kets -- 9.7 Uniform Lattices. 9.7.1 Derivative Operators -- 9.7.2 Properties of the Derivative Operators on Uniform Lattices -- 9.7.3 Position Kets on the Five Point Uniform Lattice -- 9.7.4 Biorthogonality -- 9.8 The Frame Operator S -- 9.8.1 The Exterior Product of the Ket |1> -- with its Dual Bra Counterpart -- 9.8.2 The Exterior Product of the Ket |x> -- with its Dual Bra Counterpart -- 9.8.3 The Exterior Product of the Ket |x2> -- with its Dual Bra Counterpart -- 9.8.4 The Exterior Product of the Ket |x3> -- with its Dual Bra Counterpart -- 9.8.5 The Exterior Product of the Ket |x4> -- with its Dual Bra Counterpart -- 9.8.6 Properties of the S‐Matrices -- 9.9 The Relationship Between the Resolution of Identity and Biorthogonality -- 9.9.1 Biorthogonality Implies the Resolution of Identity -- 9.9.2 The Resolution of Identity Implies Biorthogonality -- 9.10 The Construction of the Derivative Operators by Calculating Residues -- Chapter 10 Toy Model I‐6: {Δ−3,Δ−2,Δ−1,Δ0,Δ1,Δ2,Δ3} -- 10.1 Generating Formulas for the Difference Operators by Residue Method -- 10.2 Summary of the Relevant Formulas for the Calculation of Df(k) -- Chapter 11 Toy Model I‐7: {Δ−3,Δ−2,Δ−1,Δ0,Δ1,Δ2,Δ3} -- 11.1 A Guide Through the Chapter -- 11.2 Univariate Functions on 7 Nonuniformly Distributed Lattice Points -- 11.3 Setting Up the System of Equations -- 11.4 Generating Formulas for the Derivative Operators Simply‐by‐Inspection -- 11.5 Differential and Position Coordinate Bras -- 11.6 Differential Bras -- 11.7 Position Coordinate Bras -- 11.8 Differential and Position Kets: Uniformly Distributed Lattice Points -- 11.8.1 The Seven Common Denominators -- 11.8.2 The Expression of |D(6)> -- -- 11.8.3 The Expression of |D(5)> -- -- 11.8.4 The Expression of |D(4)> -- -- 11.8.5 The Expression of |D(3)> -- -- 11.8.6 The Expression of |D(2)> -- -- 11.8.7 The Expression of |D(1)>. 11.9 The Biorthogonality and the Resolution of Identity Conditions -- 11.10 Conclusions: A Brief Philosophical Detour -- Chapter 12 Toy Model II: {{−Δ1,0,Δ1},{−Δ2,0,Δ2}} -- 12.1 Introduction -- 12.2 Determination of the Expansion Coefficients F(m,n) (m,n& -- equals -- 0,1,2) -- 12.2.1 On the Construction of |1> -- -- 12.2.2 On the Construction of |x> -- -- 12.2.3 On the Construction of |y> -- -- 12.2.4 On the Construction of |x2> -- -- 12.2.5 On the Construction of |xy> -- -- 12.2.6 On the Construction of |y2> -- -- 12.2.7 On the Construction of |x2y> -- -- 12.2.8 On the Construction of |xy2> -- -- 12.2.9 On the Construction of |x2y2> -- -- 12.3 The Biorthonormality Property -- 12.4 The Resolution of Identity -- Chapter 13 Toy Model III: {−Δ1,Δ1} × {−Δ2,Δ2} × {−Δ3,Δ3} -- 13.1 Discrete Taylor Transform and Inverse Transform of Trivariate Functions -- 13.2 Determination of the Expansion Coefficients F(m,n,p) (m,n,p& -- equals -- 0,1,2) -- 13.2.1 Sample f(x,y,z) at the Node 1, Defined by the Coordinates (−Δ1,−Δ2,−Δ3) -- 13.2.2 Sample f(x,y,z) at the Node 2 Defined by the Coordinates (0,−Δ2,−Δ3) -- 13.2.3 Sample f(x,y,z) at the Node 3 Defined by the Coordinates (Δ1,−Δ2,−Δ3) -- 13.2.4 Sample f(x,y,z) at the Node 4 Defined by the Coordinates (−Δ1,0,−Δ3) -- 13.2.5 Sample f(x,y,z) at the Node 5 Defined by the Coordinates (0,0,−Δ3) -- 13.2.6 Sample f(x,y,z) at the Node 6 Defined by the Coordinates (Δ1,0,−Δ3) -- 13.2.7 Sample f(x,y,z) at the Node 7 Defined by the Coordinates (−Δ1,Δ2,−Δ3) -- 13.2.8 Sample f(x,y,z) at the Node 8 Defined by the Coordinates (0,Δ2,−Δ3) -- 13.2.9 Sample f(x,y,z) at the Node 9 Defined by the Coordinates (Δ1,Δ2,−Δ3) -- 13.2.10 Sample f(x,y,z) at the Node 10 Defined by the Coordinates (−Δ1,−Δ2,0) -- 13.2.11 Sample f(x,y,z) at the Node 11 Defined by the Coordinates (0,−Δ2,0). 13.2.12 Sample f(x,y,z) at the Node 12 Defined by the Coordinates (Δ1,−Δ2,0). |
| Record Nr. | UNINA-9910913799003321 |
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Baghai-Wadji Alireza
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| Newark : , : John Wiley & Sons, Incorporated, , 2024 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Flat extensions of positive moment matrices : recursively generated relations / / Raúl E. Curto, Lawrence A. Fialkow
| Flat extensions of positive moment matrices : recursively generated relations / / Raúl E. Curto, Lawrence A. Fialkow |
| Autore | Curto Raúl E. <1954-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1998] |
| Descrizione fisica | 1 online resource (73 p.) |
| Disciplina |
510 s
515/.723 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Moment problems (Mathematics)
Functions of complex variables Matrices |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0237-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Flat Extensions for Moment Matrices""; ""Chapter 3. The Singular Quartic Moment Problem""; ""Chapter 4. The Algebraic Variety of γ""; ""Chapter 5. J.E. McCarthy's Phenomenon and the Proof of Theorem 1.5""; ""Summary of Results""; ""Bibliography""; ""List of Symbols"" |
| Record Nr. | UNINA-9910478888703321 |
|
Curto Raúl E. <1954->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1998] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Flat extensions of positive moment matrices : recursively generated relations / / Raúl E. Curto, Lawrence A. Fialkow
| Flat extensions of positive moment matrices : recursively generated relations / / Raúl E. Curto, Lawrence A. Fialkow |
| Autore | Curto Raúl E. <1954-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [1998] |
| Descrizione fisica | 1 online resource (73 p.) |
| Disciplina |
510 s
515/.723 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Moment problems (Mathematics)
Functions of complex variables Matrices |
| ISBN | 1-4704-0237-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""Chapter 1. Introduction""; ""Chapter 2. Flat Extensions for Moment Matrices""; ""Chapter 3. The Singular Quartic Moment Problem""; ""Chapter 4. The Algebraic Variety of γ""; ""Chapter 5. J.E. McCarthy's Phenomenon and the Proof of Theorem 1.5""; ""Summary of Results""; ""Bibliography""; ""List of Symbols"" |
| Record Nr. | UNINA-9910788736503321 |
|
Curto Raúl E. <1954->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [1998] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
