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Harmonic, Wavelet and P-Adic Analysis

Author: N. M. Chuong

Publisher: World Scientific

Published: 2007

Total Pages: 393

ISBN-13: 9812770704

The mutual influence between mathematics and science and technology is becoming more and more widespread with profound connections among them being discovered. In particular, important connections between harmonic analysis, wavelet analysis and p-adic analysis have been found recently. This volume reports these findings and guides the reader towards the latest areas for further research. It is divided into two parts: harmonic, wavelet and p-adic analysis and p-adic and stochastic analysis.

Harmonic, Wavelet and P-Adic Analysis

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ISBN-13: 9814476005

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Harmonic, Wavelet and P-adic Analysis

Author: Nguyen Minh Chuong

Publisher: World Scientific

Published: 2007

Total Pages: 393

ISBN-13: 981270549X

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Four Short Courses on Harmonic Analysis

Author: Brigitte Forster

Publisher: Springer Science & Business Media

Published: 2010

Total Pages: 265

ISBN-13: 0817648909

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Written by internationally renowned mathematicians, this state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field. The work is the first one that combines spline theory, wavelets, frames, and time-frequency methods leading up to a construction of wavelets on manifolds other than Rn. Four Short Courses on Harmonic Analysis is intended as a graduate-level textbook for courses or seminars on harmonic analysis and its applications. The work is also an excellent reference or self-study guide for researchers and practitioners with diverse mathematical backgrounds working in different fields such as pure and applied mathematics, image and signal processing engineering, mathematical physics, and communication theory.

Pseudodifferential Operators and Wavelets over Real and p-adic Fields

Author: Nguyen Minh Chuong

Publisher: Springer

Published: 2018-11-28

Total Pages: 368

ISBN-13: 3319774735

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This monograph offers a self-contained introduction to pseudodifferential operators and wavelets over real and p-adic fields. Aimed at graduate students and researchers interested in harmonic analysis over local fields, the topics covered in this book include pseudodifferential operators of principal type and of variable order, semilinear degenerate pseudodifferential boundary value problems (BVPs), non-classical pseudodifferential BVPs, wavelets and Hardy spaces, wavelet integral operators, and wavelet solutions to Cauchy problems over the real field and the p-adic field.

Antieigenvalue Analysis

Author: Karl Gustafson

Publisher: World Scientific

Published: 2012

Total Pages: 259

ISBN-13: 9814366285

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Karl Gustafson is the creater of the theory of antieigenvalue analysis. Its applications spread through fields as diverse as numerical analysis, wavelets, statistics, quantum mechanics, and finance. Antieigenvalue analysis, with its operator trigonometry, is a unifying language which enables new and deeper geometrical understanding of essentially every result in operator theory and matrix theory, together with their applications. This book will open up its methods to a wide range of specialists.

Wavelet Analysis on Local Fields of Positive Characteristic

Author: Biswaranjan Behera

Publisher: Springer Nature

Published: 2022-01-01

Total Pages: 345

ISBN-13: 9811678812

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This book discusses the theory of wavelets on local fields of positive characteristic. The discussion starts with a thorough introduction to topological groups and local fields. It then provides a proof of the existence and uniqueness of Haar measures on locally compact groups. It later gives several examples of locally compact groups and describes their Haar measures. The book focuses on multiresolution analysis and wavelets on a local field of positive characteristic. It provides characterizations of various functions associated with wavelet analysis such as scaling functions, wavelets, MRA-wavelets and low-pass filters. Many other concepts which are discussed in details are biorthogonal wavelets, wavelet packets, affine and quasi-affine frames, MSF multiwavelets, multiwavelet sets, generalized scaling sets, scaling sets, unconditional basis properties of wavelets and shift invariant spaces.

Analysis, Applications, and Computations

Author: Uwe Kähler

Publisher: Springer Nature

Published: 2023-12-01

Total Pages: 696

ISBN-13: 3031363752

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This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium. The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.

Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory

Author: Palle Jorgensen

Publisher: World Scientific

Published: 2021-01-15

Total Pages: 253

ISBN-13: 9811225796

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The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.

Wavelet Theory and Harmonic Analysis in Applied Sciences

Author: Carlos E. D'Attellis

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 352

ISBN-13: 1461220106

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The idea of this book originated in the works presented at the First Latinamerican Conference on Mathematics in Industry and Medicine, held in Buenos Aires, Argentina, from November 27 to December 1, 1995. A variety of topics were discussed at this meeting. A large percentage of the papers focused on Wavelet and Harmonic Analysis. The theory and applications of this topic shown at the Conference were interesting enough to be published. Based on that we selected some works which make the core of this book. Other papers are contributions written by invited experts in the field to complete the presentation. All the works were written after the Conference. The purpose of this book is to present recent results as well as theo retical applied aspects of the subject. We have decided not to include a section devoted to the theoretical foundations of wavelet methods for non specialists. There are excellent introductions already available, for example, Chapter one in Wavelets in Medicine and Biology, edited by A. Aldroubi and M. Unser, 1996, or some of the references cited in the chapter.