Generalized Functions, Volume 3: Theory of Differential Equations
About this Title
I. M. Gel′fand and G. E. Shilov. Translated by Meinhard E. Mayer
Publication: AMS Chelsea Publishing
Publication Year: 1967; Volume 379
ISBNs: 978-1-4704-2661-3 (print); 978-1-4704-3124-2 (online)
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.
Graduate students and research mathematicians interested in analysis and differential equations.
Table of Contents
- Chapter I. Spaces of type $W$
- Chapter II. Uniqueness classes for the Cauchy problem
- Chapter III. Correctness classes for the Cauchy problem
- Chapter IV. Generalized eigenfunction expansions