A Brief History of Distribution Theory
Author : Anaiah E. Krueger
Publisher :
Page : 23 pages
File Size : 13,95 MB
Release : 2007
Category :
ISBN :
Author : Anaiah E. Krueger
Publisher :
Page : 23 pages
File Size : 13,95 MB
Release : 2007
Category :
ISBN :
Author : F. G. Friedlander
Publisher : Cambridge University Press
Page : 192 pages
File Size : 16,19 MB
Release : 1998
Category : Mathematics
ISBN : 9780521649711
The second edition of a classic graduate text on the theory of distributions.
Author : J. Lützen
Publisher : Springer
Page : 232 pages
File Size : 23,33 MB
Release : 1982-08-02
Category : Mathematics
ISBN : 9780387906478
I first learned the theory of distributions from Professor Ebbe Thue Poulsen in an undergraduate course at Aarhus University. Both his lectures and the textbook, Topological Vector Spaces, Distributions and Kernels by F. Treves, used in the course, opened my eyes to the beauty and abstract simplicity of the theory. However my incomplete study of many branches of classical analysis left me with the question: Why is the theory of distributions important? In my continued studies this question was gradually answered, but my growing interest in the history of mathematics caused me to alter my question to other questions such as: For what purpose, if any, was the theory of distributions originally created? Who invented distributions and when? I quickly found answers to the last two questions: distributions were invented by S. Sobolev and L. Schwartz around 1936 and 1950, respectively. Knowing this answer, however, only created a new question: Did Sobolev and Schwartz construct distributions from scratch or were there earlier trends and, if so, what were they? It is this question, concerning the pre history of the theory of distributions, which I attempt to answer in this book. Most of my research took place at the History of Science Department of Aarhus University. I wish to thank this department for its financial and intellectual support. I am especially grateful to Lektors Kirsti Andersen from the History of Science Department and Lars Mejlbo from the Mathematics Department, for their kindness, constructive criticism, and encouragement.
Author : J. Ian Richards
Publisher : CUP Archive
Page : 172 pages
File Size : 16,96 MB
Release : 1995-09-29
Category : Mathematics
ISBN : 9780521558907
A self-contained mathematical introduction that concentrates on the essential results important to non-specialists.
Author : Jesper Lützen
Publisher :
Page : 248 pages
File Size : 10,42 MB
Release : 1982
Category : Distribution, Theory of (Functional analysis)
ISBN :
Author : A.H. Zemanian
Publisher : Courier Corporation
Page : 404 pages
File Size : 46,24 MB
Release : 2011-11-30
Category : 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 : Israel Halperin
Publisher :
Page : 0 pages
File Size : 48,52 MB
Release : 1952
Category : Education
ISBN : 9781487591328
This pamphlet, based on lectures given by Laurent Schwartz at the Canadian Mathematical Congress in 1951, gives a detailed introduction to the theory of distributions, in terms of classical analysis, for applied mathematicians and physicists. Mathematical Congress Lecture Series, No. 1
Author : Thomas A. Severini
Publisher : Cambridge University Press
Page : 3 pages
File Size : 19,7 MB
Release : 2005-08-08
Category : Mathematics
ISBN : 1139446118
This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are covered comprehensively.
Author : Edwin Cannan
Publisher :
Page : 460 pages
File Size : 35,51 MB
Release : 1893
Category : Classical school of economics
ISBN :
Author : Gerrit Dijk
Publisher : Walter de Gruyter
Page : 120 pages
File Size : 36,28 MB
Release : 2013-03-22
Category : 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.