Volume: 379; 1967; 222 pp; Hardcover
MSC: Primary 46;
Print ISBN: 978-1-4704-2661-3
Product Code: CHEL/379.H
List Price: $50.00
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Electronic ISBN: 978-1-4704-3124-2
Product Code: CHEL/379.H.E
List Price: $50.00
AMS Member Price: $45.00
MAA Member Price: $45.00
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Generalized Functions, Volume 3: Theory of Differential Equations
Share this pageI. M. Gel′fand; G. E. Shilov
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
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. Gel′fand 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.
Readership
Graduate students and research mathematicians interested in analysis and differential equations.
Table of Contents
Table of Contents
Generalized Functions, Volume 3: Theory of Differential Equations
- Cover Cover11
- Title page iii4
- Translator’s note v6
- Preface to the Russian edition vii8
- Contents ix10
- Chapter I. Spaces of type 𝑊 112
- Chapter II. Uniqueness classes for the Cauchy problem 2940
- Chapter III. Correctness classes for the Cauchy problem 105116
- Chapter IV. Generalized eigenfunction expansions 165176
- Notes and references 211222
- Bibliography 217228
- Index 221232
- Back Cover Back Cover1234