Modulation Spaces and Nonlinear Approximation
Author | : Salti Samarah |
Publisher | : |
Total Pages | : 0 |
Release | : 1998 |
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Author | : Salti Samarah |
Publisher | : |
Total Pages | : 0 |
Release | : 1998 |
Genre | : |
ISBN | : |
Author | : Salti Samarah |
Publisher | : |
Total Pages | : 160 |
Release | : 1998 |
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Author | : Morten Nielsen |
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Total Pages | : |
Release | : 2003 |
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Author | : Lasse Borup |
Publisher | : |
Total Pages | : 20 |
Release | : 2003 |
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Release | : 2017 |
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Author | : Árpád Bényi |
Publisher | : Springer Nature |
Total Pages | : 177 |
Release | : 2020-02-22 |
Genre | : Mathematics |
ISBN | : 1071603329 |
This monograph serves as a much-needed, self-contained reference on the topic of modulation spaces. By gathering together state-of-the-art developments and previously unexplored applications, readers will be motivated to make effective use of this topic in future research. Because modulation spaces have historically only received a cursory treatment, this book will fill a gap in time-frequency analysis literature, and offer readers a convenient and timely resource. Foundational concepts and definitions in functional, harmonic, and real analysis are reviewed in the first chapter, which is then followed by introducing modulation spaces. The focus then expands to the many valuable applications of modulation spaces, such as linear and multilinear pseudodifferential operators, and dispersive partial differential equations. Because it is almost entirely self-contained, these insights will be accessible to a wide audience of interested readers. Modulation Spaces will be an ideal reference for researchers in time-frequency analysis and nonlinear partial differential equations. It will also appeal to graduate students and seasoned researchers who seek an introduction to the time-frequency analysis of nonlinear dispersive partial differential equations.
Author | : Hans Triebel |
Publisher | : European Mathematical Society |
Total Pages | : 276 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9783037190197 |
Wavelets have emerged as an important tool in analyzing functions containing discontinuities and sharp spikes. They were developed independently in the fields of mathematics, quantum physics, electrical engineering, and seismic geology. Interchanges between these fields during the last ten years have led to many new wavelet applications such as image compression, turbulence, human vision, radar, earthquake prediction, and pure mathematics applications such as solving partial differential equations. This book develops a theory of wavelet bases and wavelet frames for function spaces on various types of domains. Starting with the usual spaces on Euclidean spaces and their periodic counterparts, the exposition moves on to so-called thick domains (including Lipschitz domains and snowflake domains). Specifically, wavelet expansions and extensions to corresponding spaces on Euclidean $n$-spaces are developed. Finally, spaces on smooth and cellular domains and related manifolds are treated. Although the presentation relies on the recent theory of function spaces, basic notation and classical results are repeated in order to make the text self-contained. This book is addressed to two types of readers: researchers in the theory of function spaces who are interested in wavelets as new effective building blocks for functions and scientists who wish to use wavelet bases in classical function spaces for various applications. Adapted to the second type of reader, the preface contains a guide on where to find basic definitions and key assertions.
Author | : J-P Antoine |
Publisher | : Springer |
Total Pages | : 371 |
Release | : 2009-12-08 |
Genre | : Mathematics |
ISBN | : 3642051367 |
Partial Inner Product (PIP) Spaces are ubiquitous, e.g. Rigged Hilbert spaces, chains of Hilbert or Banach spaces (such as the Lebesgue spaces Lp over the real line), etc. In fact, most functional spaces used in (quantum) physics and in signal processing are of this type. The book contains a systematic analysis of PIP spaces and operators defined on them. Numerous examples are described in detail and a large bibliography is provided. Finally, the last chapters cover the many applications of PIP spaces in physics and in signal/image processing, respectively. As such, the book will be useful both for researchers in mathematics and practitioners of these disciplines.
Author | : Elena Cordero |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 458 |
Release | : 2020-09-21 |
Genre | : Mathematics |
ISBN | : 311053245X |
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.
Author | : Gitta Kutyniok |
Publisher | : Springer Science & Business Media |
Total Pages | : 346 |
Release | : 2012-03-07 |
Genre | : Mathematics |
ISBN | : 081768316X |
Over the last 20 years, multiscale methods and wavelets have revolutionized the field of applied mathematics by providing an efficient means of encoding isotropic phenomena. Directional multiscale systems, particularly shearlets, are now having the same dramatic impact on the encoding of multidimensional signals. Since its introduction about five years ago, the theory of shearlets has rapidly developed and gained wide recognition as the superior way of achieving a truly unified treatment in both a continuous and a digital setting. By now, it has reached maturity as a research field, with rich mathematics, efficient numerical methods, and various important applications.