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Microlocal and Time-Frequency Analysis
| Microlocal and Time-Frequency Analysis |
| Autore | Cordero Elena |
| Pubbl/distr/stampa | Basel, : MDPI - Multidisciplinary Digital Publishing Institute, 2022 |
| Descrizione fisica | 1 electronic resource (140 p.) |
| Soggetto topico |
Computing & information technology
Computer science |
| Soggetto non controllato |
pseudodifferential operators
Gevrey regularity sharp Gårding inequality p-evolution equations ultradifferentiable functions ultradistributions extended Gevrey regularity boundary values of analytic functions wave front sets Rio Papaloapan Bridge vibration signals damage identification wavelet energy accumulation method admissibility condition the continuous wavelet transform inversion formula semi-discrete wavelet transform tight frames covriance matrix polar duality uncertainty principle reconstruction problem BBM equation ill-posedness Fourier amalgam spaces Wiener amalgam spaces Fourier–Lebesgue spaces modulation spaces bounded measures convolution homogeneous Banach spaces integrated group representation Segal algebra Wiener amalgam space bounded uniform partition of unity locally compact groups |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910674035203321 |
Cordero Elena
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| Basel, : MDPI - Multidisciplinary Digital Publishing Institute, 2022 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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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 |
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Nicola Fabio
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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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. | UNINA-9910585774903321 |
|
Nicola Fabio
|
||
| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||