The Elementary Theory of Distributions
Author | : Jan Mikusiński |
Publisher | : |
Total Pages | : 58 |
Release | : 1961 |
Genre | : Functional analysis |
ISBN | : |
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Author | : Jan Mikusiński |
Publisher | : |
Total Pages | : 58 |
Release | : 1961 |
Genre | : Functional analysis |
ISBN | : |
Author | : F. G. Friedlander |
Publisher | : Cambridge University Press |
Total Pages | : 192 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 9780521649711 |
The second edition of a classic graduate text on the theory of distributions.
Author | : J. Mikusinski |
Publisher | : |
Total Pages | : |
Release | : 1957 |
Genre | : |
ISBN | : |
Author | : Jan G. Mikusiński |
Publisher | : |
Total Pages | : 46 |
Release | : 1961 |
Genre | : |
ISBN | : |
Author | : Gerrit Dijk |
Publisher | : Walter de Gruyter |
Total Pages | : 120 |
Release | : 2013-03-22 |
Genre | : Mathematics |
ISBN | : 3110298511 |
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 | : A.H. Zemanian |
Publisher | : Courier Corporation |
Total Pages | : 404 |
Release | : 2011-11-30 |
Genre | : Mathematics |
ISBN | : 0486151948 |
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 | : M.A. Al-Gwaiz |
Publisher | : CRC Press |
Total Pages | : 272 |
Release | : 1992-04-24 |
Genre | : Mathematics |
ISBN | : 9780849306693 |
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 | : Jan Mikusiński |
Publisher | : |
Total Pages | : 52 |
Release | : 1957 |
Genre | : Functional analysis |
ISBN | : |
Author | : Jan Mikusinski |
Publisher | : |
Total Pages | : |
Release | : 1957 |
Genre | : Distribution (Probability theory) |
ISBN | : |
Author | : Svetlin G. Georgiev |
Publisher | : Springer |
Total Pages | : 217 |
Release | : 2015-07-13 |
Genre | : Mathematics |
ISBN | : 3319195271 |
This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This book, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.