Hardcover ISBN:  9781470426637 
Product Code:  CHEL/381.H 
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eBook ISBN:  9781470431266 
Product Code:  CHEL/381.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9781470426637 
eBook: ISBN:  9781470431266 
Product Code:  CHEL/381.H.B 
List Price:  $134.00 $101.50 
MAA Member Price:  $120.60 $91.35 
AMS Member Price:  $120.60 $91.35 
Hardcover ISBN:  9781470426637 
Product Code:  CHEL/381.H 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $62.10 
eBook ISBN:  9781470431266 
Product Code:  CHEL/381.H.E 
List Price:  $65.00 
MAA Member Price:  $58.50 
AMS Member Price:  $58.50 
Hardcover ISBN:  9781470426637 
eBook ISBN:  9781470431266 
Product Code:  CHEL/381.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: 381; 1966; 449 ppMSC: Primary 22
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 unifying idea of Volume 5 in the series is the application of the theory of generalized functions developed in earlier volumes to problems of integral geometry, to representations of Lie groups, specifically of the Lorentz group, and to harmonic analysis on corresponding homogeneous spaces. The book is written with great clarity and requires little in the way of special previous knowledge of either group representation theory or integral geometry; it is also independent of the earlier volumes in the series. The exposition starts with the definition, properties, and main results related to the classical Radon transform, passing to integral geometry in complex space, representations of the group of complex unimodular matrices of second order, and harmonic analysis on this group and on most important homogeneous spaces related to this group. The volume ends with the study of representations of the group of real unimodular matrices of order two.
ReadershipGraduate students and research mathematicians interested in integral geometry and representation theory.
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Table of Contents

Chapters

Chapter I. Radon transform of test functions and generalized functions on a real affine space

Chapter II. Integral transforms in the complex domain

Chapter III. Representations of the group of complex unimodular matrices in two dimensions

Chapter IV. Harmonic analysis on the group of complex unimodular matrices in two dimensions

Chapter V. Integral geometry in a space of constant curvature

Chapter VI. Harmonic analysis on spaces homogeneous with respect to the Lorentz group

Chapter VII. Representations of the group of real unimodular matrices in two dimensions


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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 unifying idea of Volume 5 in the series is the application of the theory of generalized functions developed in earlier volumes to problems of integral geometry, to representations of Lie groups, specifically of the Lorentz group, and to harmonic analysis on corresponding homogeneous spaces. The book is written with great clarity and requires little in the way of special previous knowledge of either group representation theory or integral geometry; it is also independent of the earlier volumes in the series. The exposition starts with the definition, properties, and main results related to the classical Radon transform, passing to integral geometry in complex space, representations of the group of complex unimodular matrices of second order, and harmonic analysis on this group and on most important homogeneous spaces related to this group. The volume ends with the study of representations of the group of real unimodular matrices of order two.
Graduate students and research mathematicians interested in integral geometry and representation theory.

Chapters

Chapter I. Radon transform of test functions and generalized functions on a real affine space

Chapter II. Integral transforms in the complex domain

Chapter III. Representations of the group of complex unimodular matrices in two dimensions

Chapter IV. Harmonic analysis on the group of complex unimodular matrices in two dimensions

Chapter V. Integral geometry in a space of constant curvature

Chapter VI. Harmonic analysis on spaces homogeneous with respect to the Lorentz group

Chapter VII. Representations of the group of real unimodular matrices in two dimensions