Hardcover ISBN:  9781470426590 
Product Code:  CHEL/378.H 
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eBook ISBN:  9781470431235 
Product Code:  CHEL/378.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9781470426590 
eBook: ISBN:  9781470431235 
Product Code:  CHEL/378.H.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 
Hardcover ISBN:  9781470426590 
Product Code:  CHEL/378.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470431235 
Product Code:  CHEL/378.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9781470426590 
eBook ISBN:  9781470431235 
Product Code:  CHEL/378.H.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 

Book DetailsAMS Chelsea PublishingVolume: 378; 1968; 261 ppMSC: Primary 46
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 sixvolume collection, Generalized Functions, written by I. M. Gel′fand and coauthors 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.
Volume 2 is devoted to detailed study of generalized functions as linear functionals on appropriate spaces of smooth test functions. In Chapter 1, the authors introduce and study countablenormed linear topological spaces, laying out a general theoretical foundation for the analysis of spaces of generalized functions. The two most important classes of spaces of test functions are spaces of compactly supported functions and Schwartz spaces of rapidly decreasing functions. In Chapters 2 and 3 of the book, the authors transfer many results presented in Volume 1 to generalized functions corresponding to these more general spaces. Finally, Chapter 4 is devoted to the study of the Fourier transform; in particular, it includes appropriate versions of the Paley–Wiener theorem.
ReadershipGraduate students and research mathematicians interested in analysis and differential equations.
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Table of Contents

Chapters

Chapter I. Linear topological spaces

Chapter II. Fundamental and generalized functions

Chapter III. Fourier transformations of fundamental and generalized functions

Chapter IV. Spaces of type $S$

Appendix 1. Generalization of spaces of type $S$


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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 sixvolume collection, Generalized Functions, written by I. M. Gel′fand and coauthors 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.
Volume 2 is devoted to detailed study of generalized functions as linear functionals on appropriate spaces of smooth test functions. In Chapter 1, the authors introduce and study countablenormed linear topological spaces, laying out a general theoretical foundation for the analysis of spaces of generalized functions. The two most important classes of spaces of test functions are spaces of compactly supported functions and Schwartz spaces of rapidly decreasing functions. In Chapters 2 and 3 of the book, the authors transfer many results presented in Volume 1 to generalized functions corresponding to these more general spaces. Finally, Chapter 4 is devoted to the study of the Fourier transform; in particular, it includes appropriate versions of the Paley–Wiener theorem.
Graduate students and research mathematicians interested in analysis and differential equations.

Chapters

Chapter I. Linear topological spaces

Chapter II. Fundamental and generalized functions

Chapter III. Fourier transformations of fundamental and generalized functions

Chapter IV. Spaces of type $S$

Appendix 1. Generalization of spaces of type $S$