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Author: F. G. Friedlander
Publisher: Cambridge University Press
Published: 1998
Total Pages: 192
ISBN-13: 9780521649711
DOWNLOAD EBOOK →The second edition of a classic graduate text on the theory of distributions.
Author: J. Ian Richards
Publisher: CUP Archive
Published: 1995-09-29
Total Pages: 172
ISBN-13: 9780521558907
DOWNLOAD EBOOK →A self-contained mathematical introduction that concentrates on the essential results important to non-specialists.
Author: Svetlin G. Georgiev
Publisher: Springer
Published: 2015-07-13
Total Pages: 217
ISBN-13: 3319195271
DOWNLOAD EBOOK →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.
Author: J.J. Duistermaat
Publisher: Springer Science & Business Media
Published: 2010-08-09
Total Pages: 455
ISBN-13: 0817646752
DOWNLOAD EBOOK →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: Israel Halperin
Publisher:
Published: 1952
Total Pages: 0
ISBN-13: 9781487591328
DOWNLOAD EBOOK →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: J. Lützen
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 241
ISBN-13: 1461394724
DOWNLOAD EBOOK →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: Gerd Grubb
Publisher: Springer Science & Business Media
Published: 2008-10-14
Total Pages: 464
ISBN-13: 0387848940
DOWNLOAD EBOOK →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: F. Constantinescu
Publisher: Elsevier
Published: 2017-07-26
Total Pages: 159
ISBN-13: 1483150208
DOWNLOAD EBOOK →Distributions and Their Applications in Physics is the introduction of the Theory of Distributions and their applications in physics. The book contains a discussion of those topics under the Theory of Distributions that are already considered classic, which include local distributions; distributions with compact support; tempered distributions; the distribution theory in relativistic physics; and many others. The book also covers the Normed and Countably-normed Spaces; Test Function Spaces; Distribution Spaces; and the properties and operations involved in distributions. The text is recommended for physicists that wish to be acquainted with distributions and their relevance and applications as part of mathematical and theoretical physics, and for mathematicians who wish to be acquainted with the application of distributions theory for physics.
Author: Jean F. Colombeau
Publisher: Springer
Published: 2006-11-15
Total Pages: 193
ISBN-13: 3540475109
DOWNLOAD EBOOK →This book presents recent and very elementary developments of a theory of multiplication of distributions in the field of explicit and numerical solutions of systems of PDEs of physics (nonlinear elasticity, elastoplasticity, hydrodynamics, multifluid flows, acoustics). The prerequisites are kept to introductory calculus level so that the book remains accessible at the same time to pure mathematicians (as a smoothand somewhat heuristic introdcution to this theory) and to applied mathematicians, numerical engineers and theoretical physicists (as a tool to treat problems involving products of distributions).
Author: Dorina Mitrea
Publisher: Springer Science & Business Media
Published: 2013-09-20
Total Pages: 475
ISBN-13: 1461482089
DOWNLOAD EBOOK →The theory of distributions constitutes an essential tool in the study of partial differential equations. This textbook would offer, in a concise, largely self-contained form, a rapid introduction to the theory of distributions and its applications to partial differential equations, including computing fundamental solutions for the most basic differential operators: the Laplace, heat, wave, Lam\'e and Schrodinger operators.
