Generalized functions. Volume 3, Theory of differential equations / I. M. Gel'fand, G. E. Shilov ; translated by Meinhard E. Mayer.

Format:

Book

Author/Creator:

Gel'fand, I. M., author.

Shilov, G. E., author.

Contributor:

Mayer, Meinhard E., translator.

Series:

AMS Chelsea Publishing, v. 379

Standardized Title:

Obobshchennye funkt︠s︡ii. English

Language:

English

Subjects (All):

Differential equations.

Physical Description:

1 online resource (234 pages)

Edition:

[2016 edition].

Place of Publication:

Providence, Rhode Island : AMS Chelsea Publishing, 2016.

Summary:

The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gelfand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. In Volume 3, applications of generalized functions to the Cauchy problem for systems of partial differential equations with constant coefficients are considered. The book includes the study of uniqueness classes of solutions of the Cauchy problem and the study of classes of functions where the Cauchy problem is well posed. The last chapter of this volume presents results related to spectral decomposition of differential operators related to generalized eigenfunctions.

Notes:

Originally published in Russian in 1958.

Originally published in English as 5 volume set: New York : Academic Press, 1964-[1968].

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed April 11, 2017).

ISBN:

1-4704-3124-6