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Extensions of Positive Definite Functions : Applications and Their Harmonic Analysis / / by Palle Jorgensen, Steen Pedersen, Feng Tian
| Extensions of Positive Definite Functions : Applications and Their Harmonic Analysis / / by Palle Jorgensen, Steen Pedersen, Feng Tian |
| Autore | Jorgensen Palle |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 |
| Descrizione fisica | 1 online resource (XXVI, 231 p. 48 illus., 9 illus. in color.) |
| Disciplina | 515.2433 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Harmonic analysis
Topological groups Lie groups Fourier analysis Functional analysis Mathematical physics Probabilities Abstract Harmonic Analysis Topological Groups, Lie Groups Fourier Analysis Functional Analysis Mathematical Physics Probability Theory and Stochastic Processes |
| ISBN | 3-319-39780-X |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Foreword -- Preface -- Acknowledgments -- Contents -- List of Figures -- List of Tables -- Symbols -- 1 Introduction -- 1.1 Two Extension Problems -- 1.1.1 Where to Find It -- 1.2 Quantum Physics -- 1.3 Stochastic Processes -- 1.3.1 Early Roots -- 1.3.2 An Application of Lemma 1.1: A Positive Definite Function on an Infinite Dimensional Vector Space -- 1.4 Overview of Applications of RKHSs -- 1.4.1 Connections to Gaussian Processes -- 1.5 Earlier Papers -- 1.6 Organization -- 2 Extensions of Continuous Positive Definite Functions -- 2.1 The RKHS HF -- 2.1.1 An Isometry -- 2.2 The Skew-Hermitian Operator D(F) in HF -- 2.2.1 The Case of Conjugations -- 2.2.2 Illustration: G=R, Correspondence Between the Two Extension Problems -- 2.3 Enlarging the Hilbert Space -- 2.4 Ext1(F) and Ext2(F) -- 2.4.1 The Case of n=1 -- 2.4.2 Comparison of p.d. Kernels -- 2.5 Spectral Theory of D(F) and Its Extensions -- 3 The Case of More General Groups -- 3.1 Locally Compact Abelian Groups -- 3.2 Lie Groups -- 3.2.1 The GNS Construction -- 3.2.2 Local Representations -- 3.2.3 The Convex Operation in Ext(F) -- 4 Examples -- 4.1 The Case of G=Rn -- 4.2 The Case of G=R/Z -- 4.3 Example: ei2πx -- 4.4 Example: e-|x| in (-a,a), Extensions to T=R/Z -- 4.4.1 General Consideration -- 4.5 Example: e-|x| in (-a,a), Extensions to R -- 4.6 Example: A Non-extendable p.d. Function in a Neighborhood of Zero in G=R2 -- 4.6.1 A Locally Defined p.d. Functions F on G=R2 with Ext(F)=. -- 5 Type I vs. Type II Extensions -- 5.1 Pólya Extensions -- 5.2 Main Theorems -- 5.2.1 Some Applications -- 5.3 The Deficiency-Indices of D(F) -- 5.3.1 Pólya-Extensions -- 5.4 The Example 5.3, Green's Function, and an HF-ONB -- 6 Spectral Theory for Mercer Operators, and Implications for Ext(F) -- 6.1 Groups, Boundary Representations, and Renormalization -- 6.2 Shannon Sampling, and Bessel Frames.
6.3 Application: The Case of F2 and Rank-1 Perturbations -- 6.4 Positive Definite Functions, Green's Functions, and Boundary -- 6.4.1 Connection to the Energy Form Hilbert Spaces -- 7 Green's Functions -- 7.1 The RKHSs for the Two Examples F2 and F3 in Table 5.1 -- 7.1.1 Green's Functions -- 7.1.1.1 Summary: Conclusions for the Two Examples -- 7.1.2 The Case of F2(x)=1-|x|, x(-12,12) -- 7.1.2.1 Pinned Brownian Motion -- 7.1.3 The Case of F3(x)=e-|x|, x(-1,1) -- 7.1.4 Integral Kernels and Positive Definite Functions -- 7.1.5 The Ornstein-Uhlenbeck Process Revisited -- 7.1.6 An Overview of the Two Cases: F2 and F3. -- 7.2 Higher Dimensions -- 8 Comparing the Different RKHSs HF and HK -- 8.1 Applications -- 8.2 Radially Symmetric Positive Definite Functions -- 8.3 Connecting F and F When F Is a Positive Definite Function -- 8.4 The Imaginary Part of a Positive Definite Function -- 8.4.1 Connections to, and Applications of, Bochner's Theorem -- 9 Convolution Products -- 10 Models for, and Spectral Representations of, OperatorExtensions -- 10.1 Model for Restrictions of Continuous p.d. Functions on R -- 10.2 A Model of ALL Deficiency Index-(1,1) Operators -- 10.2.1 Momentum Operators in L2(0,1) -- 10.2.2 Restriction Operators -- 10.3 The Case of Indices (d,d) Where d>1 -- 10.4 Spectral Representation of Index (1,1) Hermitian Operators -- 11 Overview and Open Questions -- 11.1 From Restriction Operator to Restriction of p.d. Function -- 11.2 The Splitting HF=HF(atom)HF(ac) HF(sing) -- 11.3 The Case of G=R1 -- 11.4 The Extreme Points of Ext(F) and { F} -- References -- Index. |
| Record Nr. | UNINA-9910137138703321 |
Jorgensen Palle
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Extensions of Positive Definite Functions [e-book] : Applications and Their Harmonic Analysis / by Palle Jorgensen, Steen Pedersen, Feng Tian
| Extensions of Positive Definite Functions [e-book] : Applications and Their Harmonic Analysis / by Palle Jorgensen, Steen Pedersen, Feng Tian |
| Autore | Jorgensen, Palle |
| Pubbl/distr/stampa | Cham : Springer International Publishing, 2016 |
| Descrizione fisica | 1 online resource |
| Disciplina | 515.785 |
| Altri autori (Persone) |
Pedersen, Steenauthor
Tian, Feng |
| Collana | Lecture Notes in Mathematics, 0075-8434 ; 2160 |
| Soggetto topico |
Topological groups
Lie groups Harmonic analysis Fourier analysis Functional analysis Probabilities Mathematical physics |
| ISBN | 9783319397801 |
| Classificazione |
AMS 42-02
AMS 47-02 AMS 47B65 LC QA403-403 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991003555109707536 |
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Jorgensen, Palle
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| Cham : Springer International Publishing, 2016 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Extensions of positive-definite distributions and maximum entropy / / Jean-Pierre Gabardo
| Extensions of positive-definite distributions and maximum entropy / / Jean-Pierre Gabardo |
| Autore | Gabardo Jean-Pierre <1958-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1993 |
| Descrizione fisica | 1 online resource (111 p.) |
| Disciplina | 515/.2433 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Fourier analysis
Positive-definite functions Maximum entropy method |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0066-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""Abstract""; ""Introduction""; ""Notation""; ""1. The discrete case""; ""2. Positiveâ€?definite distributions on an interval (â€?A, A)""; ""3. The nonâ€?degenerate case""; ""4. A closure problem in L[sup(2)][sub(Î?)(R)""; ""5. Entropy maximizing measures in M [sub(A)](Q)""; ""6. Uniqueness of the extension""; ""References"" |
| Record Nr. | UNINA-9910480680903321 |
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Gabardo Jean-Pierre <1958->
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| Providence, Rhode Island : , : American Mathematical Society, , 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Extensions of positive-definite distributions and maximum entropy / / Jean-Pierre Gabardo
| Extensions of positive-definite distributions and maximum entropy / / Jean-Pierre Gabardo |
| Autore | Gabardo Jean-Pierre <1958-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1993 |
| Descrizione fisica | 1 online resource (111 p.) |
| Disciplina | 515/.2433 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Fourier analysis
Positive-definite functions Maximum entropy method |
| ISBN | 1-4704-0066-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""Abstract""; ""Introduction""; ""Notation""; ""1. The discrete case""; ""2. Positiveâ€?definite distributions on an interval (â€?A, A)""; ""3. The nonâ€?degenerate case""; ""4. A closure problem in L[sup(2)][sub(Î?)(R)""; ""5. Entropy maximizing measures in M [sub(A)](Q)""; ""6. Uniqueness of the extension""; ""References"" |
| Record Nr. | UNINA-9910788879903321 |
|
Gabardo Jean-Pierre <1958->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Extensions of positive-definite distributions and maximum entropy / / Jean-Pierre Gabardo
| Extensions of positive-definite distributions and maximum entropy / / Jean-Pierre Gabardo |
| Autore | Gabardo Jean-Pierre <1958-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 1993 |
| Descrizione fisica | 1 online resource (111 p.) |
| Disciplina | 515/.2433 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Fourier analysis
Positive-definite functions Maximum entropy method |
| ISBN | 1-4704-0066-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | ""Contents""; ""Abstract""; ""Introduction""; ""Notation""; ""1. The discrete case""; ""2. Positiveâ€?definite distributions on an interval (â€?A, A)""; ""3. The nonâ€?degenerate case""; ""4. A closure problem in L[sup(2)][sub(Î?)(R)""; ""5. Entropy maximizing measures in M [sub(A)](Q)""; ""6. Uniqueness of the extension""; ""References"" |
| Record Nr. | UNINA-9910817226403321 |
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Gabardo Jean-Pierre <1958->
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| Providence, Rhode Island : , : American Mathematical Society, , 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Extreme Eigen values of Toeplitz operators / / I. I. Jr. Hirschman and D. E. Hughes
| Extreme Eigen values of Toeplitz operators / / I. I. Jr. Hirschman and D. E. Hughes |
| Autore | Hirschman I. I (Isidore Isaac), <1922-1990, > |
| Edizione | [1st ed. 1977.] |
| Pubbl/distr/stampa | Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [1977] |
| Descrizione fisica | 1 online resource (VIII, 148 p.) |
| Disciplina | 510 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Eigenvalues
Asymptotic expansions Fourier analysis |
| ISBN | 3-540-37439-6 |
| Classificazione |
47B35
47A10 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Hilbert space background — Small eigen values -- The fourier transform theorem -- The fourier series theorem -- Hilbert space theory — Large eigen values -- The fourier series and fourier transform theorems. |
| Record Nr. | UNISA-996466488303316 |
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Hirschman I. I (Isidore Isaac), <1922-1990, >
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| Berlin, Germany ; ; New York, New York : , : Springer-Verlag, , [1977] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Extreme eigen values of Toeplitz operators / I. I. Hirschman jr., Daniel E. Hughes
| Extreme eigen values of Toeplitz operators / I. I. Hirschman jr., Daniel E. Hughes |
| Autore | Hirschman, I. I. jr. |
| Pubbl/distr/stampa | Berlin ; New York : Springer-Verlag, 1977 |
| Descrizione fisica | 145 p. ; 24 cm. |
| Disciplina | 515.724 |
| Altri autori (Persone) | Hughes, Daniel Edward |
| Collana | Lecture notes in mathematics, 0075-8434 ; 618 |
| Soggetto topico |
Asymptotic expansions
Eigenvalues Fourier analysis Operator theory Toeplitz operators |
| ISBN | 3540071474 |
| Classificazione |
AMS 47-02
AMS 47A10 AMS 47B35 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000884019707536 |
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Hirschman, I. I. jr.
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| Berlin ; New York : Springer-Verlag, 1977 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Faber Systems and Their Use in Sampling, Discrepancy, Numerical Integration [[electronic resource] /] / Hans Triebel
| Faber Systems and Their Use in Sampling, Discrepancy, Numerical Integration [[electronic resource] /] / Hans Triebel |
| Autore | Triebel Hans |
| Pubbl/distr/stampa | Zuerich, Switzerland, : European Mathematical Society Publishing House, 2012 |
| Descrizione fisica | 1 online resource (115 pages) |
| Collana | EMS Series of Lectures in Mathematics (ELM) |
| Soggetto topico |
Functional analysis
Approximations and expansions Fourier analysis Computer science |
| ISBN | 3-03719-607-6 |
| Classificazione | 46-xx41-xx42-xx68-xx |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910151927203321 |
|
Triebel Hans
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| Zuerich, Switzerland, : European Mathematical Society Publishing House, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Families of exponentials : the method of moments in controllability problems for distributed parameter systems / Sergei A. Avdonin, Sergei A. Ivanov
| Families of exponentials : the method of moments in controllability problems for distributed parameter systems / Sergei A. Avdonin, Sergei A. Ivanov |
| Autore | Avdonin, Sergei A. |
| Pubbl/distr/stampa | Cambridge : Cambridge University Press, 1995 |
| Descrizione fisica | xv, 302 p. ; 23 cm. |
| Disciplina | 515.2433 |
| Altri autori (Persone) | Ivanov, Sergei A. |
| Soggetto topico |
Control theory
Distributed parameter systems Exponential families Fourier analysis Moments method |
| ISBN | 0521452430 |
| Classificazione |
AMS 42A65
AMS 42A70 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000885369707536 |
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Avdonin, Sergei A.
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| Cambridge : Cambridge University Press, 1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
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Fastperiodische Funktionen / W. Maak
| Fastperiodische Funktionen / W. Maak |
| Autore | Maak, Wilhelm |
| Edizione | [2. korrigierte Aufl] |
| Pubbl/distr/stampa | Berlin : Springer-Verlag, 1967 |
| Descrizione fisica | viii, 240 p. ; 24 cm. |
| Disciplina | 515.5 |
| Collana | Grundlehren der mathematischen Wissenschaften = A series of comprehensive studies in mathematics, 0072-7830 ; 61 |
| Soggetto topico |
Almost periodic functions
Fourier analysis |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | ger |
| Record Nr. | UNISALENTO-991000886419707536 |
|
Maak, Wilhelm
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| Berlin : Springer-Verlag, 1967 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Soggetto topico
-
Fourier analysis
(331)
- Fourier Analysis (150)
- Functional analysis (53)
- Harmonic analysis (53)
- Partial differential equations (45)