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Product Code:  SURV/39.R.S 
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eBook ISBN:  9781470412661 
Product Code:  SURV/39.R.E 
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Softcover ISBN:  9781470479091 
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Product Code:  SURV/39.R.S.B 
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Softcover ISBN:  9781470479091 
Product Code:  SURV/39.R.S 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470412661 
Product Code:  SURV/39.R.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470479091 
eBook ISBN:  9781470412661 
Product Code:  SURV/39.R.S.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 39; 2008; 637 ppMSC: Primary 43; 53; 22; 44; 32; Secondary 31; 35
This book gives the first systematic exposition of geometric analysis on Riemannian symmetric spaces and its relationship to the representation theory of Lie groups. The book starts with modern integral geometry for double fibrations and treats several examples in detail. After discussing the theory of Radon transforms and Fourier transforms on symmetric spaces, inversion formulas, and range theorems, Helgason examines applications to invariant differential equations on symmetric spaces, existence theorems, and explicit solution formulas, particularly potential theory and wave equations. The canonical multitemporal wave equation on a symmetric space is included. The book concludes with a chapter on eigenspace representations—that is, representations on solution spaces of invariant differential equations. Known for his highquality expositions, Helgason received the 1988 Steele Prize for his earlier books Differential Geometry, Lie Groups and Symmetric Spaces and Groups and Geometric Analysis. Containing exercises (with solutions) and references to further results, this revised edition would be suitable for advanced graduate courses in modern integral geometry, analysis on Lie groups, and representation theory of Lie groups.
ReadershipGraduate students and research mathematicians interested in analysis on symmetric spaces and the representation theory of Lie groups.

Table of Contents

Chapters

I. A duality in integral geometry

II. A duality for symmetric spaces

III. The Fourier transform on a symmetric space

IV. The Radon transform on $X$ and on $X_o$. Range questions

V. Differential equations on symmetric spaces

VI. Eigenspace representations


Additional Material

Reviews

[This book] is a model of fine scholarship and must rank as a definitive source for the indicated material.
MAA Reviews 
The exposition, which emphasizes the geometric and analytic side of the subject, is selfcontained and very clear. It is good that this standard in the field, with its wealth of material, has become available again through a second edition.
EMS Newsletter 
The book is written in the elegant form that was typical for the style of S. Helgason. ... The bibliography updates and completes the previous references. The book will be of interest for both students and specialists in harmonic analysis on homogeneous spaces, integral geometry and invariant differential equations on symmetric spaces.
Zentralblatt MATH 
This monograph constitutes an important reference book for anyone working on the analysis of symmetric spaces.
Mathematical Reviews


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This book gives the first systematic exposition of geometric analysis on Riemannian symmetric spaces and its relationship to the representation theory of Lie groups. The book starts with modern integral geometry for double fibrations and treats several examples in detail. After discussing the theory of Radon transforms and Fourier transforms on symmetric spaces, inversion formulas, and range theorems, Helgason examines applications to invariant differential equations on symmetric spaces, existence theorems, and explicit solution formulas, particularly potential theory and wave equations. The canonical multitemporal wave equation on a symmetric space is included. The book concludes with a chapter on eigenspace representations—that is, representations on solution spaces of invariant differential equations. Known for his highquality expositions, Helgason received the 1988 Steele Prize for his earlier books Differential Geometry, Lie Groups and Symmetric Spaces and Groups and Geometric Analysis. Containing exercises (with solutions) and references to further results, this revised edition would be suitable for advanced graduate courses in modern integral geometry, analysis on Lie groups, and representation theory of Lie groups.
Graduate students and research mathematicians interested in analysis on symmetric spaces and the representation theory of Lie groups.

Chapters

I. A duality in integral geometry

II. A duality for symmetric spaces

III. The Fourier transform on a symmetric space

IV. The Radon transform on $X$ and on $X_o$. Range questions

V. Differential equations on symmetric spaces

VI. Eigenspace representations

[This book] is a model of fine scholarship and must rank as a definitive source for the indicated material.
MAA Reviews 
The exposition, which emphasizes the geometric and analytic side of the subject, is selfcontained and very clear. It is good that this standard in the field, with its wealth of material, has become available again through a second edition.
EMS Newsletter 
The book is written in the elegant form that was typical for the style of S. Helgason. ... The bibliography updates and completes the previous references. The book will be of interest for both students and specialists in harmonic analysis on homogeneous spaces, integral geometry and invariant differential equations on symmetric spaces.
Zentralblatt MATH 
This monograph constitutes an important reference book for anyone working on the analysis of symmetric spaces.
Mathematical Reviews