Hardcover ISBN:  9781470426583 
Product Code:  CHEL/377.H 
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eBook ISBN:  9781470431228 
Product Code:  CHEL/377.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9781470426583 
eBook: ISBN:  9781470431228 
Product Code:  CHEL/377.H.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 
Hardcover ISBN:  9781470426583 
Product Code:  CHEL/377.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470431228 
Product Code:  CHEL/377.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9781470426583 
eBook ISBN:  9781470431228 
Product Code:  CHEL/377.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: 377; 1964; 423 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 1 is devoted to basics of the theory of generalized functions. The first chapter contains main definitions and most important properties of generalized functions as functional on the space of smooth functions with compact support. The second chapter talks about the Fourier transform of generalized functions. In Chapter 3, definitions and properties of some important classes of generalized functions are discussed; in particular, generalized functions supported on submanifolds of lower dimension, generalized functions associated with quadratic forms, and homogeneous generalized functions are studied in detail. Many simple basic examples make this book an excellent place for a novice to get acquainted with the theory of generalized functions. A long appendix presents basics of generalized functions of complex variables.
ReadershipGraduate students and research mathematicians interested in analysis.
This item is also available as part of a set: 
Table of Contents

Chapters

Chapter I. Definition and simplest properties of generalized functions

Chapter II. Fourier transforms of generalized functions

Chapter III. Particular types of generalized functions

Summary of fundamental definitions and equations of volume I

Table of Fourier transforms

Appendix A. Proof of the completeness of the generalizedfunction space

Appendix B. Generalized functions of complex variables

Notes and references to the literature


Additional Material

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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 1 is devoted to basics of the theory of generalized functions. The first chapter contains main definitions and most important properties of generalized functions as functional on the space of smooth functions with compact support. The second chapter talks about the Fourier transform of generalized functions. In Chapter 3, definitions and properties of some important classes of generalized functions are discussed; in particular, generalized functions supported on submanifolds of lower dimension, generalized functions associated with quadratic forms, and homogeneous generalized functions are studied in detail. Many simple basic examples make this book an excellent place for a novice to get acquainted with the theory of generalized functions. A long appendix presents basics of generalized functions of complex variables.
Graduate students and research mathematicians interested in analysis.

Chapters

Chapter I. Definition and simplest properties of generalized functions

Chapter II. Fourier transforms of generalized functions

Chapter III. Particular types of generalized functions

Summary of fundamental definitions and equations of volume I

Table of Fourier transforms

Appendix A. Proof of the completeness of the generalizedfunction space

Appendix B. Generalized functions of complex variables

Notes and references to the literature