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The abc-problem for Gabor systems / / Xin-Rong Dai, Qiyu Sun
| The abc-problem for Gabor systems / / Xin-Rong Dai, Qiyu Sun |
| Autore | Dai Xin-Rong <1971-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2016] |
| Descrizione fisica | 1 online resource (116 pages) : illustrations |
| Disciplina | 515/.2433 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Wavelets (Mathematics)
Gabor transforms Matrices |
| Soggetto genere / forma | Electronic books. |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Gabor frames and infinite matrices -- Maximal invariant sets -- Piecewise linear transformations -- Maximal invariant sets with irrational time shifts -- Maximal invariant sets with rational time shifts -- The abc-problem for Gabor systems -- Appendix A. Algorithm -- Appendix B. Uniform sampling of signals in a shift-invariant space -- Bibliography. |
| Record Nr. | UNINA-9910480903803321 |
Dai Xin-Rong <1971->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The abc-problem for Gabor systems / / Xin-Rong Dai, Qiyu Sun
| The abc-problem for Gabor systems / / Xin-Rong Dai, Qiyu Sun |
| Autore | Dai Xin-Rong <1971-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2016] |
| Descrizione fisica | 1 online resource (116 pages) : illustrations |
| Disciplina | 515/.2433 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Wavelets (Mathematics)
Gabor transforms Matrices |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Gabor frames and infinite matrices -- Maximal invariant sets -- Piecewise linear transformations -- Maximal invariant sets with irrational time shifts -- Maximal invariant sets with rational time shifts -- The abc-problem for Gabor systems -- Appendix A. Algorithm -- Appendix B. Uniform sampling of signals in a shift-invariant space -- Bibliography. |
| Record Nr. | UNINA-9910788446203321 |
|
Dai Xin-Rong <1971->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The abc-problem for Gabor systems / / Xin-Rong Dai, Qiyu Sun
| The abc-problem for Gabor systems / / Xin-Rong Dai, Qiyu Sun |
| Autore | Dai Xin-Rong <1971-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2016] |
| Descrizione fisica | 1 online resource (116 pages) : illustrations |
| Disciplina | 515/.2433 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Wavelets (Mathematics)
Gabor transforms Matrices |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Introduction -- Gabor frames and infinite matrices -- Maximal invariant sets -- Piecewise linear transformations -- Maximal invariant sets with irrational time shifts -- Maximal invariant sets with rational time shifts -- The abc-problem for Gabor systems -- Appendix A. Algorithm -- Appendix B. Uniform sampling of signals in a shift-invariant space -- Bibliography. |
| Record Nr. | UNINA-9910827818303321 |
|
Dai Xin-Rong <1971->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Frames and harmonic analysis : AMS special sessions on frames, wavelets, and Gabor systems and frames, harmonic analysis, and operator theory, April 16-17, 2016, North Dakota State University, Fargo, North Dakota / / Yeonhyang Kim [and three others], editors
| Frames and harmonic analysis : AMS special sessions on frames, wavelets, and Gabor systems and frames, harmonic analysis, and operator theory, April 16-17, 2016, North Dakota State University, Fargo, North Dakota / / Yeonhyang Kim [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (xii, 343 pages) |
| Disciplina | 515/.63 |
| Collana | Contemporary Mathematics |
| Soggetto topico |
Frames (Vector analysis)
Harmonic analysis Wavelets (Mathematics) Gabor transforms Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Nontrigonometric harmonic analysis Information and communication, circuits -- Communication, information -- Communication, information Linear and multilinear algebra; matrix theory -- Basic linear algebra -- Basic linear algebra Operator theory -- General theory of linear operators -- General theory of linear operators Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Harmonic analysis in one variable Functional analysis -- Inner product spaces and their generalizations, Hilbert spaces -- Inner product spaces and their generalizations, Hilbert spaces Abstract harmonic analysis -- Abstract harmonic analysis -- Abstract harmonic analysis Approximations and expansions -- Approximations and expansions -- Approximations and expansions |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-4723-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910478950903321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Frames and harmonic analysis : AMS special sessions on frames, wavelets, and Gabor systems and frames, harmonic analysis, and operator theory, April 16-17, 2016, North Dakota State University, Fargo, North Dakota / / Yeonhyang Kim [and three others], editors
| Frames and harmonic analysis : AMS special sessions on frames, wavelets, and Gabor systems and frames, harmonic analysis, and operator theory, April 16-17, 2016, North Dakota State University, Fargo, North Dakota / / Yeonhyang Kim [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (xii, 343 pages) |
| Disciplina | 515/.63 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Frames (Vector analysis)
Harmonic analysis Wavelets (Mathematics) Gabor transforms Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Nontrigonometric harmonic analysis Information and communication, circuits -- Communication, information -- Communication, information Linear and multilinear algebra; matrix theory -- Basic linear algebra -- Basic linear algebra Operator theory -- General theory of linear operators -- General theory of linear operators Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Harmonic analysis in one variable Functional analysis -- Inner product spaces and their generalizations, Hilbert spaces -- Inner product spaces and their generalizations, Hilbert spaces Abstract harmonic analysis -- Abstract harmonic analysis -- Abstract harmonic analysis Approximations and expansions -- Approximations and expansions -- Approximations and expansions |
| ISBN | 1-4704-4723-1 |
| Classificazione | 15AXX41AXX42AXX42CXX43AXX46CXX47AXX94AXX |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910796857603321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Frames and harmonic analysis : AMS special sessions on frames, wavelets, and Gabor systems and frames, harmonic analysis, and operator theory, April 16-17, 2016, North Dakota State University, Fargo, North Dakota / / Yeonhyang Kim [and three others], editors
| Frames and harmonic analysis : AMS special sessions on frames, wavelets, and Gabor systems and frames, harmonic analysis, and operator theory, April 16-17, 2016, North Dakota State University, Fargo, North Dakota / / Yeonhyang Kim [and three others], editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2018] |
| Descrizione fisica | 1 online resource (xii, 343 pages) |
| Disciplina | 515/.63 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Frames (Vector analysis)
Harmonic analysis Wavelets (Mathematics) Gabor transforms Harmonic analysis on Euclidean spaces -- Nontrigonometric harmonic analysis -- Nontrigonometric harmonic analysis Information and communication, circuits -- Communication, information -- Communication, information Linear and multilinear algebra; matrix theory -- Basic linear algebra -- Basic linear algebra Operator theory -- General theory of linear operators -- General theory of linear operators Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Harmonic analysis in one variable Functional analysis -- Inner product spaces and their generalizations, Hilbert spaces -- Inner product spaces and their generalizations, Hilbert spaces Abstract harmonic analysis -- Abstract harmonic analysis -- Abstract harmonic analysis Approximations and expansions -- Approximations and expansions -- Approximations and expansions |
| ISBN | 1-4704-4723-1 |
| Classificazione | 15AXX41AXX42AXX42CXX43AXX46CXX47AXX94AXX |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910826297303321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2018] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Gabor and wavelet frames [[electronic resource] /] / editors, Say Song Goh, Amos Ron, Zuowei Shen
| Gabor and wavelet frames [[electronic resource] /] / editors, Say Song Goh, Amos Ron, Zuowei Shen |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2007 |
| Descrizione fisica | 1 online resource (228 p.) |
| Disciplina | 515/.723 |
| Altri autori (Persone) |
GohSay Song
RonAmos ShenZuowei |
| Collana | Lecture notes series |
| Soggetto topico |
Gabor transforms
Wavelets (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-91871-7
9786611918712 981-270-908-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONTENTS; Foreword; Preface; A Guided Tour from Linear Algebra to the Foundations of Gabor Analysis Hans G. Feichtinger, Franz Luef and Tobias Werther; 1. Introduction; 2. Basics in Linear Algebra; 3. Finite Dimensional Gabor Analysis; 4. Frames and Riesz Bases; 5. Gabor Analysis on L2; 6. Time-Frequency Representations; 7. The Gelfand Triple; 8. The Spreading Function; 9. Conclusion and Outlook; References; Some Iterative Algorithms to Compute Canonical Windows for Gabor Frames A. J. E. M. Janssen; 1. Introduction; 2. Overview; 3. Basic Tools; 4. Analysis of Recursion I to Approximate gt
5. Proposing Iterations Without Inversions 5.1. Iterations for gt; 5.2. Iterations for gd; 6. Analysis of Recursion II to Approximate gt; 7. Analysis of Recursion IV to Approximate gd; 8. Summary of Results for Iterations III and V; 9. Concluding Remarks; Acknowledgments; References; Gabor Analysis, Noncommutative Tori and Feichtinger's Algebra Franz Luef; 1. Introduction; 2. Operator Algebras of Time-Frequency Shifts; 3. Noncommutative Tori and Feichtinger's Algebra; 4. Feichtinger's Algebra as Bimodule for C ( ) and C ( 0) 5. Application to Gabor Analysis: Biorthogonality Relation of Wexler-Raz 6. Conclusions; Acknowledgment; References; Unitary Matrix Functions,Wavelet Algorithms, and Structural Properties of Wavelets Palle E. T. Jorgensen; 1. Introduction; 1.1. Index of terminology in mathematics and in engineering; 1.2. Motivation; 1.2.1. Some points of history; 1.2.2. Some early applications; 2. Signal Processing; 2.1. Filters in communications engineering; 2.2. Algorithms for signals and for wavelets; 2.2.2. Subdivision algorithms; 2.2.3. Wavelet packet algorithms 2.2.4. Lifting algorithms: Sweldens and more 2.3. Factorization theorems for matrix functions; 2.3.1. The case of polynomial functions [the polyphase matrix, joint work with Ola Bratteli]; 2.3.2. General results in mathematics on matrix functions; 2.3.3. Connection between matrix functions and wavelets; 2.3.3.1. Multiresolution wavelets; 2.3.3.2. Generalized multiresolutions [joint work with L. Baggett, K. Merrill, and J. Packer]; 2.3.4. Matrix completion; 2.3.5. Connections between matrix functions and signal processing; Acknowledgments; References Unitary Systems, Wavelet Sets, and Operator-Theoretic Interpolation of Wavelets and Frames David R. Larson 1. Introduction; 1.1. Talks and abstracts; 1.2. Some background; 1.2.1. Interpolation; 1.2.2. Some basic terminology; 1.2.3. Acknowledgements; 2. Unitary Systems and Wavelet Sets; 2.1. The one-dimensional wavelet system; 2.1.1. Dyadic wavelets; 2.1.2. The dyadic unitary system; 2.1.3. Non-dyadic wavelets in one dimension; 2.2. N dimensions; 2.2.1. The expansive-dilation case; 2.2.2. The non-expansive dilation case; 2.3. Abstract systems; 2.3.1. Restrictions on wandering vectors 2.3.2. Group systems |
| Record Nr. | UNINA-9910450691203321 |
| Hackensack, NJ, : World Scientific, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Gabor and wavelet frames [[electronic resource] /] / editors, Say Song Goh, Amos Ron, Zuowei Shen
| Gabor and wavelet frames [[electronic resource] /] / editors, Say Song Goh, Amos Ron, Zuowei Shen |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2007 |
| Descrizione fisica | 1 online resource (228 p.) |
| Disciplina | 515/.723 |
| Altri autori (Persone) |
GohSay Song
RonAmos ShenZuowei |
| Collana | Lecture notes series |
| Soggetto topico |
Gabor transforms
Wavelets (Mathematics) |
| ISBN |
1-281-91871-7
9786611918712 981-270-908-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONTENTS; Foreword; Preface; A Guided Tour from Linear Algebra to the Foundations of Gabor Analysis Hans G. Feichtinger, Franz Luef and Tobias Werther; 1. Introduction; 2. Basics in Linear Algebra; 3. Finite Dimensional Gabor Analysis; 4. Frames and Riesz Bases; 5. Gabor Analysis on L2; 6. Time-Frequency Representations; 7. The Gelfand Triple; 8. The Spreading Function; 9. Conclusion and Outlook; References; Some Iterative Algorithms to Compute Canonical Windows for Gabor Frames A. J. E. M. Janssen; 1. Introduction; 2. Overview; 3. Basic Tools; 4. Analysis of Recursion I to Approximate gt
5. Proposing Iterations Without Inversions 5.1. Iterations for gt; 5.2. Iterations for gd; 6. Analysis of Recursion II to Approximate gt; 7. Analysis of Recursion IV to Approximate gd; 8. Summary of Results for Iterations III and V; 9. Concluding Remarks; Acknowledgments; References; Gabor Analysis, Noncommutative Tori and Feichtinger's Algebra Franz Luef; 1. Introduction; 2. Operator Algebras of Time-Frequency Shifts; 3. Noncommutative Tori and Feichtinger's Algebra; 4. Feichtinger's Algebra as Bimodule for C ( ) and C ( 0) 5. Application to Gabor Analysis: Biorthogonality Relation of Wexler-Raz 6. Conclusions; Acknowledgment; References; Unitary Matrix Functions,Wavelet Algorithms, and Structural Properties of Wavelets Palle E. T. Jorgensen; 1. Introduction; 1.1. Index of terminology in mathematics and in engineering; 1.2. Motivation; 1.2.1. Some points of history; 1.2.2. Some early applications; 2. Signal Processing; 2.1. Filters in communications engineering; 2.2. Algorithms for signals and for wavelets; 2.2.2. Subdivision algorithms; 2.2.3. Wavelet packet algorithms 2.2.4. Lifting algorithms: Sweldens and more 2.3. Factorization theorems for matrix functions; 2.3.1. The case of polynomial functions [the polyphase matrix, joint work with Ola Bratteli]; 2.3.2. General results in mathematics on matrix functions; 2.3.3. Connection between matrix functions and wavelets; 2.3.3.1. Multiresolution wavelets; 2.3.3.2. Generalized multiresolutions [joint work with L. Baggett, K. Merrill, and J. Packer]; 2.3.4. Matrix completion; 2.3.5. Connections between matrix functions and signal processing; Acknowledgments; References Unitary Systems, Wavelet Sets, and Operator-Theoretic Interpolation of Wavelets and Frames David R. Larson 1. Introduction; 1.1. Talks and abstracts; 1.2. Some background; 1.2.1. Interpolation; 1.2.2. Some basic terminology; 1.2.3. Acknowledgements; 2. Unitary Systems and Wavelet Sets; 2.1. The one-dimensional wavelet system; 2.1.1. Dyadic wavelets; 2.1.2. The dyadic unitary system; 2.1.3. Non-dyadic wavelets in one dimension; 2.2. N dimensions; 2.2.1. The expansive-dilation case; 2.2.2. The non-expansive dilation case; 2.3. Abstract systems; 2.3.1. Restrictions on wandering vectors 2.3.2. Group systems |
| Record Nr. | UNINA-9910777059403321 |
| Hackensack, NJ, : World Scientific, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Gabor and wavelet frames / / editors, Say Song Goh, Amos Ron, Zuowei Shen
| Gabor and wavelet frames / / editors, Say Song Goh, Amos Ron, Zuowei Shen |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2007 |
| Descrizione fisica | 1 online resource (228 p.) |
| Disciplina | 515/.723 |
| Altri autori (Persone) |
GohSay Song
RonAmos ShenZuowei |
| Collana | Lecture notes series |
| Soggetto topico |
Gabor transforms
Wavelets (Mathematics) |
| ISBN |
1-281-91871-7
9786611918712 981-270-908-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
CONTENTS; Foreword; Preface; A Guided Tour from Linear Algebra to the Foundations of Gabor Analysis Hans G. Feichtinger, Franz Luef and Tobias Werther; 1. Introduction; 2. Basics in Linear Algebra; 3. Finite Dimensional Gabor Analysis; 4. Frames and Riesz Bases; 5. Gabor Analysis on L2; 6. Time-Frequency Representations; 7. The Gelfand Triple; 8. The Spreading Function; 9. Conclusion and Outlook; References; Some Iterative Algorithms to Compute Canonical Windows for Gabor Frames A. J. E. M. Janssen; 1. Introduction; 2. Overview; 3. Basic Tools; 4. Analysis of Recursion I to Approximate gt
5. Proposing Iterations Without Inversions 5.1. Iterations for gt; 5.2. Iterations for gd; 6. Analysis of Recursion II to Approximate gt; 7. Analysis of Recursion IV to Approximate gd; 8. Summary of Results for Iterations III and V; 9. Concluding Remarks; Acknowledgments; References; Gabor Analysis, Noncommutative Tori and Feichtinger's Algebra Franz Luef; 1. Introduction; 2. Operator Algebras of Time-Frequency Shifts; 3. Noncommutative Tori and Feichtinger's Algebra; 4. Feichtinger's Algebra as Bimodule for C ( ) and C ( 0) 5. Application to Gabor Analysis: Biorthogonality Relation of Wexler-Raz 6. Conclusions; Acknowledgment; References; Unitary Matrix Functions,Wavelet Algorithms, and Structural Properties of Wavelets Palle E. T. Jorgensen; 1. Introduction; 1.1. Index of terminology in mathematics and in engineering; 1.2. Motivation; 1.2.1. Some points of history; 1.2.2. Some early applications; 2. Signal Processing; 2.1. Filters in communications engineering; 2.2. Algorithms for signals and for wavelets; 2.2.2. Subdivision algorithms; 2.2.3. Wavelet packet algorithms 2.2.4. Lifting algorithms: Sweldens and more 2.3. Factorization theorems for matrix functions; 2.3.1. The case of polynomial functions [the polyphase matrix, joint work with Ola Bratteli]; 2.3.2. General results in mathematics on matrix functions; 2.3.3. Connection between matrix functions and wavelets; 2.3.3.1. Multiresolution wavelets; 2.3.3.2. Generalized multiresolutions [joint work with L. Baggett, K. Merrill, and J. Packer]; 2.3.4. Matrix completion; 2.3.5. Connections between matrix functions and signal processing; Acknowledgments; References Unitary Systems, Wavelet Sets, and Operator-Theoretic Interpolation of Wavelets and Frames David R. Larson 1. Introduction; 1.1. Talks and abstracts; 1.2. Some background; 1.2.1. Interpolation; 1.2.2. Some basic terminology; 1.2.3. Acknowledgements; 2. Unitary Systems and Wavelet Sets; 2.1. The one-dimensional wavelet system; 2.1.1. Dyadic wavelets; 2.1.2. The dyadic unitary system; 2.1.3. Non-dyadic wavelets in one dimension; 2.2. N dimensions; 2.2.1. The expansive-dilation case; 2.2.2. The non-expansive dilation case; 2.3. Abstract systems; 2.3.1. Restrictions on wandering vectors 2.3.2. Group systems |
| Record Nr. | UNINA-9910807912503321 |
| Hackensack, NJ, : World Scientific, c2007 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Wave packet analysis of Feynman path integrals / / Fabio Nicola, S. Ivan Trapasso
| Wave packet analysis of Feynman path integrals / / Fabio Nicola, S. Ivan Trapasso |
| Autore | Nicola Fabio |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2022] |
| Descrizione fisica | 1 online resource (220 pages) |
| Disciplina | 515.43 |
| Collana | Lecture notes in mathematics |
| Soggetto topico |
Feynman integrals
Gabor transforms Quantum theory Integrals de Feynman Teoria quàntica |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-031-06186-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- Outline -- 1 Itinerary: How Gabor Analysis Met Feynman Path Integrals -- 1.1 The Elements of Gabor Analysis -- 1.1.1 The Analysis of Functions via Gabor Wave Packets -- 1.2 The Analysis of Operators via Gabor Wave Packets -- 1.2.1 The Problem of Quantization -- 1.2.2 Metaplectic Operators -- 1.3 The Problem of Feynman Path Integrals -- 1.3.1 Rigorous Time-Slicing Approximation of Feynman Path Integrals -- 1.3.2 Pointwise Convergence at the Level of Integral Kernels for Feynman-Trotter Parametrices -- 1.3.3 Convergence of Time-Slicing Approximations in L(L2) for Low-Regular Potentials -- 1.3.4 Convergence of Time-Slicing Approximations in the Lp Setting -- Part I Elements of Gabor Analysis -- 2 Basic Facts of Classical Analysis -- 2.1 General Notation -- 2.2 Function Spaces -- 2.2.1 Lebesgue Spaces -- 2.2.2 Differentiable Functions and Distributions -- 2.3 Basic Operations on Functions and Distributions -- 2.4 The Fourier Transform -- 2.4.1 Convolution and Fourier Multipliers -- 2.5 Some More Facts and Notations -- 3 The Gabor Analysis of Functions -- 3.1 Time-Frequency Representations -- 3.1.1 The Short-Time Fourier Transform -- 3.1.2 Quadratic Representations -- 3.2 Modulation Spaces -- 3.3 Wiener Amalgam Spaces -- 3.4 A Banach-Gelfand Triple of Modulation Spaces -- 3.5 The Sjöstrand Class and Related Spaces -- 3.6 Complements -- 3.6.1 Weight Functions -- 3.6.2 The Cohen Class of Time-Frequency Representations -- 3.6.3 Kato-Sobolev Spaces -- 3.6.4 Fourier Multipliers -- 3.6.5 More on the Sjöstrand Class -- 3.6.6 Boundedness of Time-Frequency Transforms on Modulation Spaces -- 3.6.7 Gabor Frames -- 4 The Gabor Analysis of Operators -- 4.1 The General Program -- 4.2 The Weyl Quantization -- 4.3 Metaplectic Operators -- 4.3.1 Notable Facts on Symplectic Matrices.
4.3.2 Metaplectic Operators: Definitions and Basic Properties -- 4.3.3 The Schrödinger Equation with Quadratic Hamiltonian -- 4.3.4 Symplectic Covariance of the Weyl Calculus -- 4.3.5 Gabor Matrix of Metaplectic Operators -- 4.4 Fourier and Oscillatory Integral Operators -- 4.4.1 Canonical Transformations and the Associated Operators -- 4.4.2 Generalized Metaplectic Operators -- 4.4.3 Oscillatory Integral Operators with Rough Amplitude -- 4.5 Complements -- 4.5.1 Weyl Operators and Narrow Convergence -- 4.5.2 General Quantization Rules -- 4.5.3 The Class FIO'(S,vs) -- 4.5.4 Finer Aspects of Gabor Wave Packet Analysis -- 5 Semiclassical Gabor Analysis -- 5.1 Semiclassical Transforms and Function Spaces -- 5.1.1 Sobolev Spaces and Embeddings -- 5.2 Semiclassical Quantization, Metaplectic Operators and FIOs -- Part II Analysis of Feynman Path Integrals -- 6 Pointwise Convergence of the Integral Kernels -- 6.1 Summary -- 6.2 Preliminary Results -- 6.2.1 The Schwartz Kernel Theorem -- 6.2.2 Uniform Estimates for Linear Changes of Variable -- 6.2.3 Exponentiation in Banach Algebras -- 6.2.4 Two Technical Lemmas -- 6.3 Reduction to the Case .12em.1emdotteddotteddotted.76dotted.6h=(2π)-1 -- 6.4 The Fundamental Solution and the Trotter Formula -- 6.5 Potentials in M∞0,s -- 6.6 Potentials in C∞b -- 6.7 Potentials in the Sjöstrand Class M∞,1 -- 6.8 Convergence at Exceptional Times -- 6.9 Physics at Exceptional Times -- 7 Convergence in L(L2) for Potentials in the Sjöstrand Class -- 7.1 Summary -- 7.2 An Abstract Approximation Result in L(L2) -- 7.3 Short-Time Analysis of the Action -- 7.4 Estimates for the Parametrix and Convergence Results -- 8 Convergence in L(L2) for Potentials in Kato-Sobolev Spaces -- 8.1 Summary -- 8.2 Sobolev Regularity of the Hamiltonian Flow -- 8.3 Sobolev Regularity of the Classical Action. 8.4 Analysis of the Parametrices and Convergence Results -- 8.5 Higher-Order Parametrices -- 9 Convergence in the Lp Setting -- 9.1 Summary -- 9.2 Review of the Short Time Analysis in the Smooth Category -- 9.3 Wave Packet Analysis of the Schrödinger Flow -- 9.4 Convergence in Lp with Loss of Derivatives -- 9.5 The Case of Magnetic Fields -- 9.6 Sharpness of the Results -- 9.7 Extensions to the Case of Rough Potentials -- Bibliography -- Index. |
| Record Nr. | UNISA-996483172503316 |
|
Nicola Fabio
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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