A Course In Distribution Theory And Applications
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A Course In Distribution Theory And Applications
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Author : R. S. Pathak
language : en
Publisher: CRC Press
Release Date : 2001
A Course In Distribution Theory And Applications written by R. S. Pathak and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The book covers important topics: basic properties of distributions, convolution, Fourier transforms, Sobolev spaces, weak solutions, distributions on locally convex spaces and on differentiable manifolds. It is a largely self-contained text.".
Distribution Theory And Transform Analysis
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Author : A.H. Zemanian
language : en
Publisher: Courier Corporation
Release Date : 2011-11-30
Distribution Theory And Transform Analysis written by A.H. Zemanian and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-30 with Mathematics categories.
Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.
Distribution Theory And Applications
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Author : Abdellah El Kinani
language : en
Publisher: World Scientific
Release Date : 2010
Distribution Theory And Applications written by Abdellah El Kinani and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
The general frame for the resolution of PDEs is the theory of kernels ù the first elements of which are sufficient to show the practicality of distribution theory in applications. --
A Guide To Distribution Theory And Fourier Transforms
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Author : Robert S Strichartz
language : en
Publisher: World Scientific Publishing Company
Release Date : 2003-06-13
A Guide To Distribution Theory And Fourier Transforms written by Robert S Strichartz and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-13 with Mathematics categories.
This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book. A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.
Distribution Theory
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Author : Gerrit Dijk
language : en
Publisher: Walter de Gruyter
Release Date : 2013-03-22
Distribution Theory written by Gerrit Dijk and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-22 with Mathematics categories.
The theory of distributions has numerous applications and is extensively used in mathematics, physics and engineering. There is however relatively little elementary expository literature on distribution theory. This book is intended as an introduction. Starting with the elementary theory of distributions, it proceeds to convolution products of distributions, Fourier and Laplace transforms, tempered distributions, summable distributions and applications. The theory is illustrated by several examples, mostly beginning with the case of the real line and then followed by examples in higher dimensions. This is a justified and practical approach, it helps the reader to become familiar with the subject. A moderate number of exercises are added. It is suitable for a one-semester course at the advanced undergraduate or beginning graduate level or for self-study.
Distributions
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Author : J.J. Duistermaat
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-09
Distributions written by J.J. Duistermaat 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 2010-08-09 with Mathematics categories.
This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background.
Distribution Theory Of Runs And Patterns And Its Applications
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Author : James C. Fu
language : en
Publisher: World Scientific
Release Date : 2003
Distribution Theory Of Runs And Patterns And Its Applications written by James C. Fu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
A rigorous, comprehensive introduction to the finite Markov chain imbedding technique for studying the distributions of runs and patterns from a unified and intuitive viewpoint, away from the lines of traditional combinatorics.
The Theory Of Distributions
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Author : J. Ian Richards
language : en
Publisher: CUP Archive
Release Date : 1995-09-29
The Theory Of Distributions written by J. Ian Richards and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-29 with Mathematics categories.
A self-contained mathematical introduction that concentrates on the essential results important to non-specialists.
Theory Of Distributions
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Author : M.A. Al-Gwaiz
language : en
Publisher: CRC Press
Release Date : 1992-04-24
Theory Of Distributions written by M.A. Al-Gwaiz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-04-24 with Mathematics categories.
A textbook for a graduate course in the theory of distributions and related topics, for students of applied mathematics or theoretical physics. Introduces the theory, explicates mathematical structures and the Hilbert-space aspects, and presents applications to typical boundary problems. Annotation
Distributions Theory And Applications
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Author : Johannes Jisse Duistermaat
language : en
Publisher:
Release Date : 2009
Distributions Theory And Applications written by Johannes Jisse Duistermaat and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.