Hardcover ISBN:  9781470426620 
Product Code:  CHEL/380.H 
List Price:  $69.00 
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eBook ISBN:  9781470431259 
Product Code:  CHEL/380.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9781470426620 
eBook: ISBN:  9781470431259 
Product Code:  CHEL/380.H.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 
Hardcover ISBN:  9781470426620 
Product Code:  CHEL/380.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470431259 
Product Code:  CHEL/380.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9781470426620 
eBook ISBN:  9781470431259 
Product Code:  CHEL/380.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: 380; 1964; 384 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.
The main goal of Volume 4 is to develop the functional analysis setup for the universe of generalized functions. The main notion introduced in this volume is the notion of rigged Hilbert space (also known as the equipped Hilbert space, or Gelfand triple). Such space is, in fact, a triple of topological vector spaces \(E \subset H \subset E'\), where \(H\) is a Hilbert space, \(E'\) is dual to \(E\), and inclusions \(E\subset H\) and \(H\subset E'\) are nuclear operators. The book is devoted to various applications of this notion, such as the theory of positive definite generalized functions, the theory of generalized stochastic processes, and the study of measures on linear topological spaces.
ReadershipGraduate students and research mathematicians interested in functional analysis.
This item is also available as part of a set: 
Table of Contents

Chapters

Chapter I. The kernel theorem. Nuclear spaces. Rigged Hilbert space

Chapter II. Positive and positivedefinite generalized functions

Chapter III. Generalized random processes

Chapter IV. Measures in linear topological spaces


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.
The main goal of Volume 4 is to develop the functional analysis setup for the universe of generalized functions. The main notion introduced in this volume is the notion of rigged Hilbert space (also known as the equipped Hilbert space, or Gelfand triple). Such space is, in fact, a triple of topological vector spaces \(E \subset H \subset E'\), where \(H\) is a Hilbert space, \(E'\) is dual to \(E\), and inclusions \(E\subset H\) and \(H\subset E'\) are nuclear operators. The book is devoted to various applications of this notion, such as the theory of positive definite generalized functions, the theory of generalized stochastic processes, and the study of measures on linear topological spaces.
Graduate students and research mathematicians interested in functional analysis.

Chapters

Chapter I. The kernel theorem. Nuclear spaces. Rigged Hilbert space

Chapter II. Positive and positivedefinite generalized functions

Chapter III. Generalized random processes

Chapter IV. Measures in linear topological spaces