A Course in Distribution Theory and Applications PDF Download

Author: R. S. Pathak
Publisher: CRC Press
ISBN: 9780849309816
Category : Mathematics
Languages : en
Pages : 168

View

Book Description
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.".

Author: J.J. Duistermaat
Publisher: Springer Science & Business Media
ISBN: 0817646752
Category : Mathematics
Languages : en
Pages : 445

View

Book Description
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.

Author: R. S. Pathak
Publisher: Alpha Science Int'l Ltd.
ISBN: 9781842650202
Category : Mathematics
Languages : en
Pages : 162

View

Book Description
Provides basic ideas and results of distribution theory and its applications to Fourier analysis and partial differential equations. Examples are provided to illustrate the concepts; exercises of various level of difficulty are given. Important topics covered like basic properties of distributions, convolution, Fourier transforms, Sobolev spaces, weak solutions, distributions on locally convex spaces and on differentiable manifolds.

Author: Robert S. Strichartz
Publisher: World Scientific
ISBN: 9789812384300
Category : Mathematics
Languages : en
Pages : 238

View

Book Description
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.

Author: A.H. Zemanian
Publisher: Courier Corporation
ISBN: 0486151948
Category : Mathematics
Languages : en
Pages : 400

View

Book Description
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.

Author: Gerd Grubb
Publisher: Springer Science & Business Media
ISBN: 0387848940
Category : Mathematics
Languages : en
Pages : 464

View

Book Description
This book gives an introduction to distribution theory, based on the work of Schwartz and of many other people. It is the first book to present distribution theory as a standard text. Each chapter has been enhanced with many exercises and examples.

Author: J. Ian Richards
Publisher: CUP Archive
ISBN: 9780521558907
Category : Mathematics
Languages : en
Pages : 172

View

Book Description
A self-contained mathematical introduction that concentrates on the essential results important to non-specialists.

Author: Gerrit Dijk
Publisher: Walter de Gruyter
ISBN: 3110298511
Category : Mathematics
Languages : en
Pages : 120

View

Book Description
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.

Author: M.A. Al-Gwaiz
Publisher: CRC Press
ISBN: 0849306698
Category : Mathematics
Languages : en
Pages : 276

View

Book Description
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

Author: Abdellah El Kinani
Publisher: World Scientific
ISBN: 9814304921
Category : Mathematics
Languages : en
Pages : 219

View

Book Description
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. --