Wavelet Analysis On Local Fields Of Positive Characteristic

Author : Biswaranjan Behera,Qaiser Jahan
Publisher : Unknown
Page : 0 pages
File Size : 45,6 Mb
Release : 2021
Category : Electronic
ISBN : 9811678820

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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. .

Author : Biswaranjan Behera,Qaiser Jahan
Publisher : Springer Nature
Page : 345 pages
File Size : 42,7 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.

Author : Lokenath Debnath,Firdous Ahmad Shah
Publisher : Springer
Page : 553 pages
File Size : 41,6 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.

Author : Lokenath Debnath,Firdous A. Shah
Publisher : Birkhäuser
Page : 220 pages
File Size : 53,8 Mb
Release : 2017-09-05
Category : Mathematics
ISBN : 9783319594330

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Lecture Notes on Wavelet Transforms by Lokenath Debnath,Firdous A. Shah Pdf

This book provides a systematic exposition of the basic ideas and results of wavelet analysis suitable for mathematicians, scientists, and engineers alike. The primary goal of this text is to show how different types of wavelets can be constructed, illustrate why they are such powerful tools in mathematical analysis, and demonstrate their use in applications. It also develops the required analytical knowledge and skills on the part of the reader, rather than focus on the importance of more abstract formulation with full mathematical rigor. These notes differs from many textbooks with similar titles in that a major emphasis is placed on the thorough development of the underlying theory before introducing applications and modern topics such as fractional Fourier transforms, windowed canonical transforms, fractional wavelet transforms, fast wavelet transforms, spline wavelets, Daubechies wavelets, harmonic wavelets and non-uniform wavelets. The selection, arrangement, and presentation of the material in these lecture notes have carefully been made based on the authors’ teaching, research and professional experience. Drafts of these lecture notes have been used successfully by the authors in their own courses on wavelet transforms and their applications at the University of Texas Pan-American and the University of Kashmir in India.

Author : Yu. A. Farkov,Pammy Manchanda,Abul Hasan Siddiqi
Publisher : Springer
Page : 381 pages
File Size : 54,8 Mb
Release : 2019-04-29
Category : Mathematics
ISBN : 9789811363702

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Construction of Wavelets Through Walsh Functions by Yu. A. Farkov,Pammy Manchanda,Abul Hasan Siddiqi Pdf

This book focuses on the fusion of wavelets and Walsh analysis, which involves non-trigonometric function series (or Walsh–Fourier series). The primary objective of the book is to systematically present the basic properties of non-trigonometric orthonormal systems such as the Haar system, Haar–Vilenkin system, Walsh system, wavelet system and frame system, as well as updated results on the book’s main theme. Based on lectures that the authors presented at several international conferences, the notions and concepts introduced in this interdisciplinary book can be applied to any situation where wavelets and their variants are used. Most of the applications of wavelet analysis and Walsh analysis can be tried for newly constructed wavelets. Given its breadth of coverage, the book offers a valuable resource for theoreticians and those applying mathematics in diverse areas. It is especially intended for graduate students of mathematics and engineering and researchers interested in applied analysis.

Author : Khalil Ahmad,Abdullah
Publisher : Springer
Page : 238 pages
File Size : 54,8 Mb
Release : 2018-06-21
Category : Mathematics
ISBN : 9789811302688

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Wavelet Packets and Their Statistical Applications by Khalil Ahmad,Abdullah Pdf

This book presents the basic concepts of functional analysis, wavelet analysis and thresholding. It begins with an elementary chapter on preliminaries such as basic concepts of functional analysis, a brief tour of the wavelet transform, Haar scaling functions and function space, wavelets, symlets wavelets and coiflets wavelets. In turn, Chapters 2 and 3 address the construction of wavelet packets, selected results on wavelet packets, band-limited wavelet packets, characterisations of wavelet packets, multiresolution analysis (MRA) wavelet packets, pointwise convergence, the convergence of wavelet packet series and convolution bounds. Chapter 4 discusses characterisations of function spaces like Lebesgue spaces, Hardy spaces and Sobolev spaces in terms of wavelet packets, while Chapter 5 is devoted to applications of wavelets and wavelet packets in speech denoising and biomedical signals. In closing, Chapter 6 highlights applications of wavelets and wavelet packets in image denoising.

Author : Sandeep Singh,Mehmet Ali Sarigöl,Alka Munjal
Publisher : Springer Nature
Page : 242 pages
File Size : 42,9 Mb
Release : 2023-01-16
Category : Mathematics
ISBN : 9783031190827

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Algebra, Analysis, and Associated Topics by Sandeep Singh,Mehmet Ali Sarigöl,Alka Munjal Pdf

The chapters in this contributed volume explore new results and existing problems in algebra, analysis, and related topics. This broad coverage will help generate new ideas to solve various challenges that face researchers in pure mathematics. Specific topics covered include maximal rotational hypersurfaces, k-Horadam sequences, quantum dynamical semigroups, and more. Additionally, several applications of algebraic number theory and analysis are presented. Algebra, Analysis, and Associated Topics will appeal to researchers, graduate students, and engineers interested in learning more about the impact pure mathematics has on various fields.

Author : Jieyun Bai,Haibo Ni,Jichao Zhao
Publisher : Frontiers Media SA
Page : 379 pages
File Size : 46,8 Mb
Release : 2023-09-13
Category : Science
ISBN : 9782832533871

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Diagnosis, Monitoring, and Treatment of Heart Rhythm: New Insights and Novel Computational Methods by Jieyun Bai,Haibo Ni,Jichao Zhao Pdf

Author : M. H. Taibleson
Publisher : Princeton University Press
Page : 308 pages
File Size : 43,6 Mb
Release : 2015-03-08
Category : Mathematics
ISBN : 9781400871339

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Fourier Analysis on Local Fields. (MN-15) by M. H. Taibleson Pdf

This book presents a development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications. The force of the analogy between the local field and Euclidean cases rests in the relationship of the field structures that underlie the respective cases. A complete classification of locally compact, non-discrete fields gives us two examples of connected fields (real and complex numbers); the rest are local fields (p-adic numbers, p-series fields, and their algebraic extensions). The local fields are studied in an effort to extend knowledge of the reals and complexes as locally compact fields. The author's central aim has been to present the basic facts of Fourier analysis on local fields in an accessible form and in the same spirit as in Zygmund's Trigonometric Series (Cambridge, 1968) and in Introduction to Fourier Analysis on Euclidean Spaces by Stein and Weiss (1971). Originally published in 1975. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : Yunfei Chen,Xiaodong Liu,Lipo Wang,Chunlei Ji,Qiang Sun,Yuan Ren,Xin Wang
Publisher : CRC Press
Page : 226 pages
File Size : 45,9 Mb
Release : 2015-09-17
Category : Computers
ISBN : 9781315651491

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Systems and Computer Technology by Yunfei Chen,Xiaodong Liu,Lipo Wang,Chunlei Ji,Qiang Sun,Yuan Ren,Xin Wang Pdf

This volume consists of papers presented at the 2014 International Symposium on Systems and Computer Technology (ISSCT 2014, Shanghai, China, 15-17 November 2014). The demand for systems and informatics have been constantly increasing, as more and more computer applications have been built. Great efforts have been made to improve the state of the a

Author : John J. Benedetto
Publisher : CRC Press
Page : 590 pages
File Size : 45,9 Mb
Release : 1993-09-27
Category : Mathematics
ISBN : 0849382718

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Wavelets by John J. Benedetto Pdf

Wavelets is a carefully organized and edited collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. The construction of wavelet bases and the fast computation of the wavelet transform in both continuous and discrete settings is covered. The theory of frames, dilation equations, and local Fourier bases are also presented. The second part of the book discusses applications in signal analysis, while the third part covers operator analysis and partial differential equations. Each chapter in these sections provides an up-to-date introduction to such topics as sampling theory, probability and statistics, compression, numerical analysis, turbulence, operator theory, and harmonic analysis. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. It will be an especially useful reference for harmonic analysts, partial differential equation researchers, signal processing engineers, numerical analysts, fluids researchers, and applied mathematicians.

Author : M.W. Frazier
Publisher : Springer
Page : 517 pages
File Size : 49,7 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9783642855702

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An Introduction to Wavelets Through Linear Algebra by M.W. Frazier Pdf

Mathematics majors at Michigan State University take a "Capstone" course near the end of their undergraduate careers. The content of this course varies with each offering. Its purpose is to bring together different topics from the undergraduate curriculum and introduce students to a developing area in mathematics. This text was originally written for a Capstone course. Basic wavelet theory is a natural topic for such a course. By name, wavelets date back only to the 1980s. On the boundary between mathematics and engineering, wavelet theory shows students that mathematics research is still thriving, with important applications in areas such as image compression and the numerical solution of differential equations. The author believes that the essentials of wavelet theory are sufficiently elementary to be taught successfully to advanced undergraduates. This text is intended for undergraduates, so only a basic background in linear algebra and analysis is assumed. We do not require familiarity with complex numbers and the roots of unity.

Author : Andreĭ I︠U︡rʹevich Khrennikov,Andrei Yu. Khrennikov,Sergei V. Kozyrev,W. A. Zúñiga-Galindo
Publisher : Cambridge University Press
Page : 255 pages
File Size : 40,5 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.

Author : Daoliang Li,Zhenbo Li
Publisher : Springer
Page : 659 pages
File Size : 48,8 Mb
Release : 2016-11-11
Category : Computers
ISBN : 9783319483573

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Computer and Computing Technologies in Agriculture IX by Daoliang Li,Zhenbo Li Pdf

The two volumes IFIP AICT 478 and 479 constitute the refereed post-conference proceedings of the 9th IFIP WG 5.14 International Conference on Computer and Computing Technologies in Agriculture, CCTA 2015, held in Beijing, China, in September 2015. The 122 revised papers included in this volume were carefully selected from 237 submissions. They cover a wide range of interesting theories and applications of information technology in agriculture, including intelligent sensing, monitoring and automatic control technology; key technology and models of the Internet of things; intelligent technology for agricultural equipment; computer vision; computer graphics and virtual reality; computer simulation, optimization and modeling; cloud computing and agricultural applications; agricultural big data; decision support systems and expert systems; 3s technology and precision agriculture; quality and safety of agricultural products; detection and tracing technology; and agricultural electronic commerce technology.

Author : Charles K. Chui
Publisher : SIAM
Page : 223 pages
File Size : 47,8 Mb
Release : 1997-01-01
Category : Mathematics
ISBN : 9780898713848

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Wavelets by Charles K. Chui Pdf

Mathematically rigorous monograph on wavelets, written specifically for nonspecialists. Places the reader at the forefront of current research.