Pseudodifferential Operators And Wavelets Over Real And P Adic Fields

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Pseudodifferential Operators and Wavelets over Real and p-adic Fields

Author : Nguyen Minh Chuong
Publisher : Springer
Page : 368 pages
File Size : 45,7 Mb
Release : 2018-11-28
Category : Mathematics
ISBN : 9783319774732

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Pseudodifferential Operators and Wavelets over Real and p-adic Fields by Nguyen Minh Chuong Pdf

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.

Pseudodifferential Equations Over Non-Archimedean Spaces

Author : W. A. Zúñiga-Galindo
Publisher : Springer
Page : 186 pages
File Size : 52,8 Mb
Release : 2017-01-08
Category : Mathematics
ISBN : 9783319467382

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Pseudodifferential Equations Over Non-Archimedean Spaces by W. A. Zúñiga-Galindo Pdf

Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainly with the theory and applications of p-adic wavelets.

Ultrametric Pseudodifferential Equations and Applications

Author : Andreĭ I︠U︡rʹevich Khrennikov,Andrei Yu. Khrennikov,Sergei V. Kozyrev,W. A. Zúñiga-Galindo
Publisher : Cambridge University Press
Page : 255 pages
File Size : 51,7 Mb
Release : 2018-04-26
Category : Mathematics
ISBN : 9781107188822

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Ultrametric Pseudodifferential Equations and Applications by Andreĭ I︠U︡rʹevich Khrennikov,Andrei Yu. Khrennikov,Sergei V. Kozyrev,W. A. Zúñiga-Galindo Pdf

Provides a novel interdisciplinary perspective on the state of the art of ultrametric pseudodifferential equations and their applications.

P-adic Analysis and Mathematical Physics

Author : Vasili? Sergeevich Vladimirov,I. V. Volovich,E. I. Zelenov
Publisher : World Scientific
Page : 350 pages
File Size : 54,7 Mb
Release : 1994
Category : Science
ISBN : 9810208804

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P-adic Analysis and Mathematical Physics by Vasili? Sergeevich Vladimirov,I. V. Volovich,E. I. Zelenov Pdf

p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.

Frames and Operator Theory in Analysis and Signal Processing

Author : David R. Larson
Publisher : American Mathematical Soc.
Page : 306 pages
File Size : 40,5 Mb
Release : 2008
Category : Operator theory
ISBN : 9780821841440

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Frames and Operator Theory in Analysis and Signal Processing by David R. Larson Pdf

This volume contains articles based on talks presented at the Special Session Frames and Operator Theory in Analysis and Signal Processing, held in San Antonio, Texas, in January of 2006.

Metrics, Norms, Inner Products, and Operator Theory

Author : Christopher Heil
Publisher : Birkhäuser
Page : 359 pages
File Size : 55,5 Mb
Release : 2018-08-28
Category : Mathematics
ISBN : 9783319653228

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Metrics, Norms, Inner Products, and Operator Theory by Christopher Heil Pdf

This text is a self-contained introduction to the three main families that we encounter in analysis – metric spaces, normed spaces, and inner product spaces – and to the operators that transform objects in one into objects in another. With an emphasis on the fundamental properties defining the spaces, this book guides readers to a deeper understanding of analysis and an appreciation of the field as the “science of functions.” Many important topics that are rarely presented in an accessible way to undergraduate students are included, such as unconditional convergence of series, Schauder bases for Banach spaces, the dual of lp topological isomorphisms, the Spectral Theorem, the Baire Category Theorem, and the Uniform Boundedness Principle. The text is constructed in such a way that instructors have the option whether to include more advanced topics. Written in an appealing and accessible style, Metrics, Norms, Inner Products, and Operator Theory is suitable for independent study or as the basis for an undergraduate-level course. Instructors have several options for building a course around the text depending on the level and interests of their students. Key features: Aimed at students who have a basic knowledge of undergraduate real analysis. All of the required background material is reviewed in the first chapter. Suitable for undergraduate-level courses; no familiarity with measure theory is required. Extensive exercises complement the text and provide opportunities for learning by doing. A separate solutions manual is available for instructors via the Birkhäuser website (www.springer.com/978-3-319-65321-1). Unique text providing an undergraduate-level introduction to metrics, norms, inner products, and their associated operator theory.

Wavelet Analysis on Local Fields of Positive Characteristic

Author : Biswaranjan Behera,Qaiser Jahan
Publisher : Springer Nature
Page : 345 pages
File Size : 44,9 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9789811678813

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Wavelet Analysis on Local Fields of Positive Characteristic by Biswaranjan Behera,Qaiser Jahan Pdf

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.

The XFT Quadrature in Discrete Fourier Analysis

Author : Rafael G. Campos
Publisher : Springer
Page : 235 pages
File Size : 49,7 Mb
Release : 2019-05-24
Category : Mathematics
ISBN : 9783030134235

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The XFT Quadrature in Discrete Fourier Analysis by Rafael G. Campos Pdf

This book has two main objectives, the first of which is to extend the power of numerical Fourier analysis and to show by means of theoretical examples and numerous concrete applications that when computing discrete Fourier transforms of periodic and non periodic functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform (DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT), since the XFT matrix appears as a convergent quadrature of a more general transform, the fractional Fourier transform. In turn, the book’s second goal is to present the XFT matrix as a finite-dimensional transformation that links certain discrete operators in the same way that the corresponding continuous operators are related by the Fourier transform, and to show that the XFT matrix accordingly generates sequences of matrix operators that represent continuum operators, and which allow these operators to be studied from another perspective.

Landscapes of Time-Frequency Analysis

Author : Paolo Boggiatto,Elena Cordero,Maurice de Gosson,Hans G. Feichtinger,Fabio Nicola,Alessandro Oliaro,Anita Tabacco
Publisher : Springer
Page : 358 pages
File Size : 46,9 Mb
Release : 2019-01-30
Category : Mathematics
ISBN : 9783030052102

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Landscapes of Time-Frequency Analysis by Paolo Boggiatto,Elena Cordero,Maurice de Gosson,Hans G. Feichtinger,Fabio Nicola,Alessandro Oliaro,Anita Tabacco Pdf

The chapters in this volume are based on talks given at the inaugural Aspects of Time-Frequency Analysis conference held in Turin, Italy from July 5-7, 2017, which brought together experts in harmonic analysis and its applications. New connections between different but related areas were presented in the context of time-frequency analysis, encouraging future research and collaborations. Some of the topics covered include: Abstract harmonic analysis, Numerical harmonic analysis, Sampling theory, Compressed sensing, Mathematical signal processing, Pseudodifferential operators, and Applications of harmonic analysis to quantum mechanics. Landscapes of Time-Frequency Analysis will be of particular interest to researchers and advanced students working in time-frequency analysis and other related areas of harmonic analysis.

Topics in Classical and Modern Analysis

Author : Martha Abell,Emil Iacob,Alex Stokolos,Sharon Taylor,Sergey Tikhonov,Jiehua Zhu
Publisher : Springer Nature
Page : 373 pages
File Size : 53,7 Mb
Release : 2019-10-21
Category : Mathematics
ISBN : 9783030122775

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Topics in Classical and Modern Analysis by Martha Abell,Emil Iacob,Alex Stokolos,Sharon Taylor,Sergey Tikhonov,Jiehua Zhu Pdf

Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume. The topics included are Fourier analysis, Padè approximation, dynamical systems and difference operators, splines, Christoffel functions, best approximation, discrepancy theory and Jackson-type theorems of approximation. The articles of this collection were originated from the International Conference in Approximation Theory, held in Savannah, GA in 2017, and organized by the editors of this volume.

Numerical Fourier Analysis

Author : Gerlind Plonka,Daniel Potts,Gabriele Steidl,Manfred Tasche
Publisher : Springer
Page : 618 pages
File Size : 44,7 Mb
Release : 2019-02-05
Category : Mathematics
ISBN : 9783030043063

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Numerical Fourier Analysis by Gerlind Plonka,Daniel Potts,Gabriele Steidl,Manfred Tasche Pdf

This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods. It starts with a detailed discussion of classical Fourier theory to enable readers to grasp the construction and analysis of advanced fast Fourier algorithms introduced in the second part, such as nonequispaced and sparse FFTs in higher dimensions. Lastly, it contains a selection of numerical applications, including recent research results on nonlinear function approximation by exponential sums. The code of most of the presented algorithms is available in the authors’ public domain software packages. Students and researchers alike benefit from this unified presentation of Fourier theory and corresponding algorithms.

Theory of P-adic Distributions

Author : S. Albeverio,V. M. Shelkovich
Publisher : Cambridge University Press
Page : 369 pages
File Size : 55,5 Mb
Release : 2010-03-18
Category : Mathematics
ISBN : 9780521148566

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Theory of P-adic Distributions by S. Albeverio,V. M. Shelkovich Pdf

A wide-ranging 2010 survey of new and important topics in p-adic analysis for researchers and graduate students.

P-adic Deterministic and Random Dynamics

Author : Andrei Y. Khrennikov,Marcus Nilsson
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 48,5 Mb
Release : 2013-03-14
Category : Science
ISBN : 9781402026607

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P-adic Deterministic and Random Dynamics by Andrei Y. Khrennikov,Marcus Nilsson Pdf

This book provides an overview of the theory of p-adic (and more general non-Archimedean) dynamical systems. The main part of the book is devoted to discrete dynamical systems. It presents a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. Coverage also details p-adic neural networks and their applications to cognitive sciences: learning algorithms, memory recalling.

Harmonic, Wavelet and P-adic Analysis

Author : Nguyen Minh Chuong
Publisher : World Scientific
Page : 393 pages
File Size : 51,6 Mb
Release : 2007
Category : Science
ISBN : 9789812705495

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Harmonic, Wavelet and P-adic Analysis by Nguyen Minh Chuong Pdf

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.

Wavelet Transforms and Their Applications

Author : Lokenath Debnath,Firdous Ahmad Shah
Publisher : Springer
Page : 562 pages
File Size : 45,7 Mb
Release : 2014-11-25
Category : Technology & Engineering
ISBN : 9780817684181

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Wavelet Transforms and Their Applications by Lokenath Debnath,Firdous Ahmad Shah Pdf

This textbook is an introduction to wavelet transforms and accessible to a larger audience with diverse backgrounds and interests in mathematics, science, and engineering. Emphasis is placed on the logical development of fundamental ideas and systematic treatment of wavelet analysis and its applications to a wide variety of problems as encountered in various interdisciplinary areas. Topics and Features: * This second edition heavily reworks the chapters on Extensions of Multiresolution Analysis and Newlands’s Harmonic Wavelets and introduces a new chapter containing new applications of wavelet transforms * Uses knowledge of Fourier transforms, some elementary ideas of Hilbert spaces, and orthonormal systems to develop the theory and applications of wavelet analysis * Offers detailed and clear explanations of every concept and method, accompanied by carefully selected worked examples, with special emphasis given to those topics in which students typically experience difficulty * Includes carefully chosen end-of-chapter exercises directly associated with applications or formulated in terms of the mathematical, physical, and engineering context and provides answers to selected exercises for additional help Mathematicians, physicists, computer engineers, and electrical and mechanical engineers will find Wavelet Transforms and Their Applications an exceptionally complete and accessible text and reference. It is also suitable as a self-study or reference guide for practitioners and professionals.