Generalized Functions, Volume 3

Theory of Differential Equations

I.M. Gel'fand, G.E. Shilov (Autoren)

Buch | Hardcover

222 Seiten

2016
American Mathematical Society (Verlag)
978-1-4704-2661-3 (ISBN)

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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.

Spaces of type $W$
Uniqueness classes for the Cauchy problem
Correctness classes for the Cauchy problem
Generalized eigenfunction expansions
Notes and references
Bibliography
Index

Erscheinungsdatum	06.05.2016
Reihe/Serie	Chelsea Publications
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	574 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4704-2661-7 / 1470426617
ISBN-13	978-1-4704-2661-3 / 9781470426613
Zustand	Neuware