Info
- Utilizzare la checkbox di selezione a fianco di ciascun documento per attivare le funzionalità di stampa, invio email, download nei formati disponibili del (i) record.
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 | ||
| ||
Convolution and equidistribution : Sato-Tate theorems for finite-field Mellin transforms / / Nicholas M. Katz
| Convolution and equidistribution : 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) |
| ISBN |
9786613379962
9781283379960 1283379961 9781400842704 1400842700 |
| 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-9910968930703321 |
|
Katz Nicholas M. <1943->
|
||
| Princeton ; ; Oxford, : Princeton University Press, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Electromagnetic wave propagation in turbulence : evaluation and application of Mellin transforms / / Richard J. Sasiela
| Electromagnetic wave propagation in turbulence : evaluation and application of Mellin transforms / / Richard J. Sasiela |
| Autore | Sasiela Richard J. <1940-> |
| Edizione | [2nd ed.] |
| Pubbl/distr/stampa | Bellingham, Wash., : SPIE Press, 2007 |
| Descrizione fisica | 1 online resource (386 p.) |
| Disciplina | 539.2 |
| Collana | SPIE Press monograph |
| Soggetto topico |
Electromagnetic waves - Transmission
Atmospheric turbulence Mellin transform Numerical calculations |
| ISBN |
9781615837250
1615837256 9780819478399 0819478393 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
1. Introduction. 1.1. Book plan -- 1.2. Introduction to Mellin transforms -- 1.3. Higher transcendental functions -- 2. Basic equations for wave propagation in turbulence. 2.1. Turbulence spectra -- 2.2. Rytov approximation. -- 2.3. Phase and log-amplitude variances -- 2.4. Power spectral density -- 2.5. Beam shape and Strehl ratio -- 3. Filter functions. 3.1. Circular aperture modes -- 3.2. Piston and tilt on an annulus -- 3.3. Finite apertures and focal anisoplanatism -- 3.4. Adaptive-optics systems -- 3.5. Structure function for a distributed beacon -- 3.6. Developing new variance filter functions -- 4. Zero-parameter problems. 4.1. Turbulence models and moments -- 4.2. Tilt and piston for collimated and focused beams -- 4.3. Gradient tilt -- 4.4. Difference between gradient and Zernike tilt -- 4.5. Zernike mode variance. -- 4.6. Piston and tilt of a gaussian beam -- 4.7. Beam movement at a target -- 4.8. Angle-of-arrival jitter -- 4.9. Scintillation for collimated and focused beams -- 4.10. Phase variance with finite servo bandwidth -- 4.11. Variances for beams corrected by adaptive optics.
5. Integral evaluation with Mellin transforms. 5.1. Integral evaluation with one parameter. -- 5.2. Asymptotic solutions -- 5.3. Multiple poles -- 6. Examples with a single positive parameter. 6.1. Zernike modes and tilt for the von Karman spectrum -- 6.2. Tilt for the Greenwood spectrum -- 6.3. Tilt with finite inner scale -- 6.4. Piston- and tilt-removed phase variance on an annulus -- 6.5. Effect of diffraction on tilt -- 6.6. Tilt anisoplanatism -- 6.7. Power spectral density of tilt -- 6.8. Scintillation with finite apertures and sources -- 6.9. Scintillation with finite inner scale -- 6.10. Scintillation anisoplanatism -- 6.11. Focus anisoplanatism. -- 6.12. Zernike anisoplanatism -- 6.13. Focal anisoplanatism for point sources -- 6.14 Focal anisoplanatism for distributed sources -- 6.15 Focal anisoplanatism for offset sources -- 7. Strehl ratio. -- 7.1. Strehl ratio for propagation through turbulence -- 7.2. Strehl ratio with beam jitter -- 7.3. Strehl ratio with anisoplanatism -- 7.4. Strehl ratio for various anisoplanatic effects -- 7.5. Strehl ratio using numerical integration. -- 8. Mellin transforms with a complex parameter -- 8.1. Mellin-Barnes integrals with complex parameters -- 8.2. Asymptotic results with a complex parameter -- 8.3. The Mellin transform of an exponential times a Bessel function. 9. finite beam characteristics as examples with a single cmplex parameter -- 9.1. Phase and log-amplitude variances of beam waves -- 9.2. Power spectral density of beam waves -- 9.3. Scintillation on beam waves -- 9.4. Heuristic scintillation formulas -- 10. Mellin transforms in n complex planes -- 10.1. Convergence of multi-parameter series -- 10.2. Path closure at infinity -- 10.3. Integration in multiple complex planes -- 10.4. Asymptotic solution in two or more complex planes -- 11. integral evaluation with n parameters -- 11.1. An integral with two Bessel functions and a sinusoid -- 11.2. An integral with three Bessel functions -- 11.3. Example in three and n complex planes -- 11.4. Effect of outer scale on tilt anisoplanatism -- 11.5. Tilt with inner and outer scale -- 11.6. Power spectrum of tilt with outer scale -- 11.7. Structure and correlation functions with inner and outer scales -- 12. Beam shape -- 12.1. General formula for beam shape. -- 12.2. Beam shape for uncorrected turbulence -- 12.3. Beam shape with tilt jitter -- 12.4. Beam shape with anisoplanatism -- Appendix A: Additional Mellin transforms -- Appendix B: Transcendental functions -- Index. |
| Record Nr. | UNINA-9911004806603321 |
|
Sasiela Richard J. <1940->
|
||
| Bellingham, Wash., : SPIE Press, 2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
