Distribution Theory And Transform Analysis
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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 Transform Analysis
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Author : A. H. Zemanian
language : en
Publisher:
Release Date : 1967
Distribution Theory And Transform Analysis written by A. H. Zemanian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
Distribution Theory And Transform Analysis
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Author : Armen H.. Zemanian
language : en
Publisher:
Release Date : 1985
Distribution Theory And Transform Analysis written by Armen H.. Zemanian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Theory of distributions (Functional analysis) categories.
Distribution Theory And Transform Analysis
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Author : Armen H. Zemanian
language : it
Publisher:
Release Date : 1965
Distribution Theory And Transform Analysis written by Armen H. Zemanian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with categories.
Distribution Theory And Transform Analysis An Introd To Generalized Functions With Applications
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Author : Armen H. Zemanian
language : en
Publisher:
Release Date : 1984
Distribution Theory And Transform Analysis An Introd To Generalized Functions With Applications written by Armen H. Zemanian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.
Distribution Theory And Transform Analysis
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Author : Theodore Caplow
language : en
Publisher:
Release Date : 1965
Distribution Theory And Transform Analysis written by Theodore Caplow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with categories.
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.".
Transform Analysis Of Generalized Functions
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Author : O.P. Misra
language : en
Publisher: Elsevier
Release Date : 1986-01-01
Transform Analysis Of Generalized Functions written by O.P. Misra and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-01-01 with Mathematics categories.
Transform Analysis of Generalized Functions concentrates on finite parts of integrals, generalized functions and distributions. It gives a unified treatment of the distributional setting with transform analysis, i.e. Fourier, Laplace, Stieltjes, Mellin, Hankel and Bessel Series.Included are accounts of applications of the theory of integral transforms in a distributional setting to the solution of problems arising in mathematical physics. Information on distributional solutions of differential, partial differential equations and integral equations is conveniently collected here.The volume will serve as introductory and reference material for those interested in analysis, applications, physics and engineering.
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.
An Extension Of The Laplace Transform To Schwartz Distributions
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Author : Douglas B. Price
language : en
Publisher:
Release Date : 1974
An Extension Of The Laplace Transform To Schwartz Distributions written by Douglas B. Price and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Laplace transformation categories.
A new characterization of the Laplace transform is developed which extends the transform to the Schwartz distributions. The class of distributions includes, in addition to all ordinary functions, the impulse functions and other singular functions which occur as solutions to ordinary and partial differential equations. The standard theorems on analyticity, uniqueness, and invertibility of the transform are proved by using the new characterization as the definition of the Laplace transform. The new definition uses sequences of linear transformations on the space of distributions in a manner suggested by a paper of E. Gesztelyi which extended the Laplace transform to another class of generalized functions, the Mikusinski operators. It is shown that the new sequential definition of the transform is equivalent to Schwartz' extension of the ordinary Laplace transform to distributions but, in contrast to Schwartz' definition, does not use the distributional Fourier transform. Several theorems concerning the particular linear transformations used to define the Laplace transforms are proved. All the results proved in one dimension are extended to the n-dimensional case, but proofs are presented only for those situations that require methods different from their one-dimensional analogs.