Operator Related Function Theory And Time Frequency Analysis
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Operator Related Function Theory And Time Frequency Analysis
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Author : Karlheinz Gröchenig
language : en
Publisher: Springer
Release Date : 2014-11-25
Operator Related Function Theory And Time Frequency Analysis written by Karlheinz Gröchenig and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-25 with Mathematics categories.
This book collects the proceedings of the 2012 Abel Symposium, held at the Norwegian Academy of Science and Letters, Oslo. The Symposium, and this book, are focused on two important fields of modern mathematical analysis: operator-related function theory and time-frequency analysis; and the profound interplay between them. Among the original contributions and overview lectures gathered here are a paper presenting multifractal analysis as a bridge between geometric measure theory and signal processing; local and global geometry of Prony systems and Fourier reconstruction of piecewise-smooth functions; Bernstein's problem on weighted polynomial approximation; singular distributions and symmetry of the spectrum; and many others. Offering a selection of the latest and most exciting results obtained by world-leading researchers, the book will benefit scientists working in Harmonic and Complex Analysis, Mathematical Physics and Signal Processing.
Time Frequency Analysis Of Operators
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Author : Elena Cordero
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-09-21
Time Frequency Analysis Of Operators written by Elena Cordero and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-21 with Mathematics categories.
This authoritative text studies pseudodifferential and Fourier integral operators in the framework of time-frequency analysis, providing an elementary approach, along with applications to almost diagonalization of such operators and to the sparsity of their Gabor representations. Moreover, Gabor frames and modulation spaces are employed to study dispersive equations such as the Schrödinger, wave, and heat equations and related Strichartz problems. The first part of the book is addressed to non-experts, presenting the basics of time-frequency analysis: short time Fourier transform, Wigner distribution and other representations, function spaces and frames theory, and it can be read independently as a short text-book on this topic from graduate and under-graduate students, or scholars in other disciplines.
Foundations Of Time Frequency Analysis
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Author : Karlheinz Gröchenig
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Foundations Of Time Frequency Analysis written by Karlheinz Gröchenig and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Technology & Engineering categories.
Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.
Fourier Analysis
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Author : Michael Ruzhansky
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-18
Fourier Analysis written by Michael Ruzhansky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-18 with Mathematics categories.
This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. It is based on lectures given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland. This collection of 20 refereed articles is based on selected talks and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”
Landscapes Of Time Frequency Analysis
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Author : Paolo Boggiatto
language : en
Publisher: Springer Nature
Release Date : 2020-11-21
Landscapes Of Time Frequency Analysis written by Paolo Boggiatto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-21 with Mathematics categories.
This contributed volume features chapters based on talks given at the second international conference titled Aspects of Time-Frequency Analysis (ATFA 19), held at Politecnico di Torino from June 25th to June 27th, 2019. Written by experts in harmonic analysis and its applications, these chapters provide a valuable overview of the state-of-the-art of this active area of research. New results are collected as well, making this a valuable resource for readers seeking to be brought up-to-date. Topics covered include: Signal analysis Quantum theory Modulation space theory Applications to the medical industry Wavelet transform theory Anti-Wick operators Landscapes of Time-Frequency Analysis: ATFA 2019 will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.
The Weyl Operator And Its Generalization
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Author : Leon Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-13
The Weyl Operator And Its Generalization written by Leon Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-13 with Mathematics categories.
The discovery of quantum mechanics in the years 1925-1930 necessitated the consideration of associating ordinary functions with non-commuting operators. Methods were proposed by Born/Jordan, Kirkwood, and Weyl. Sometime later, Moyal saw the connection between the Weyl rule and the Wigner distribution, which had been proposed by Wigner in 1932 as a way of doing quantum statistical mechanics. The basic idea of associating functions with operators has since been generalized and developed to a high degree. It has found several application fields, including quantum mechanics, pseudo-differential operators, time-frequency analysis, quantum optics, wave propagation, differential equations, image processing, radar, and sonar. This book aims at bringing together the results from the above mentioned fields in a unified manner and showing the reader how the methods have been applied. A wide audience is addressed, particularly students and researchers who want to obtain an up-to-date working knowledge of the field. The mathematics is accessible to the uninitiated reader and is presented in a straightforward manner.
Pseudo Differential Operators
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Author : Luigi Rodino
language : en
Publisher: American Mathematical Soc.
Release Date : 2007-11-21
Pseudo Differential Operators written by Luigi Rodino and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-21 with Mathematics categories.
This volume is based on lectures given at the workshop on pseudo-differential operators held at the Fields Institute from December 11, 2006 to December 15, 2006. The two main themes of the workshop and hence this volume are partial differential equations and time-frequency analysis. The contents of this volume consist of five mini-courses for graduate students and post-docs, and fifteen papers on related topics. Of particular interest in this volume are the mathematical underpinnings, applications and ramifications of the relatively new Stockwell transform, which is a hybrid of the Gabor transform and the wavelet transform. The twenty papers in this volume reflect modern trends in the development of pseudo-differential operators.
Time Frequency Analysis
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Author : Boualem Boashash
language : en
Publisher: Elsevier
Release Date : 2003-10-16
Time Frequency Analysis written by Boualem Boashash and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-16 with Technology & Engineering categories.
Time Frequency Signal Analysis and Processing covers fundamental concepts, principles and techniques, treatment of specialised and advanced topics, methods and applications, including results of recent research. This book deals with the modern methodologies, key techniques and concepts that form the core of new technologies used in IT, multimedia, telecommunications as well as most fields of engineering, science and technology. It focuses on advanced techniques and methods that allow a refined extraction and processing of information, allowing efficient and effective decision making that would not be possible with classical techniques. The Author, fellow of IEEE for Pioneering contributions to time-frequency analysis and signal processing education, is an expert in the field, having written over 300 papers on the subject over a period pf 25 years. This is a REAL book, not a mere collection of specialised papers, making it essential reading for researchers and practitioners in the field of signal processing. *The most comprehensive text and reference book published on the subject, all the most up to date research on this subject in one place *Key computer procedures and code are provided to assist the reader with practical implementations and applications *This book brings together the main knowledge of time-frequency signal analysis and processing, (TFSAP), from theory and applications, in a user-friendly reference suitable for both experts and beginners
Recent Developments In Time Frequency Analysis
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Author : Leon Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-10-31
Recent Developments In Time Frequency Analysis written by Leon Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-31 with Science categories.
Recent Developments in Time-Frequency Analysis brings together in one place important contributions and up-to-date research results in this fast moving area. Recent Developments in Time-Frequency Analysis serves as an excellent reference, providing insight into some of the most challenging research issues in the field.
Function Spaces Theory And Applications
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Author : Ilia Binder
language : en
Publisher: Springer Nature
Release Date : 2024-01-12
Function Spaces Theory And Applications written by Ilia Binder and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-12 with Mathematics categories.
The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They also have several essential applications in other fields of mathematics and engineering, e.g., robust control engineering, signal and image processing, and theory of communication. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins, e.g. the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b), have also been the center of attention in the past two decades. Studying the Hilbert spaces of analytic functions and the operators acting on them, as well as their applications in other parts of mathematics or engineering were the main subjects of this program. During the program, the world leading experts on function spaces gathered and discussed the new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With more than 250 hours of lectures by prominent mathematicians, a wide variety of topics were covered. More explicitly, there were mini-courses and workshops on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Blaschke Products and Inner Functions, Discrete and Continuous Semigroups of Composition Operators, The Corona Problem, Non-commutative Function Theory, Drury-Arveson Space, and Convergence of Scattering Data and Non-linear Fourier Transform. At the end of each week, there was a high profile colloquium talk on the current topic. The program also contained two semester-long advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. The current volume features a more detailed version of some of the talks presented during the program.