**Translations of Mathematical Monographs**

1994;
265 pp;
Hardcover

MSC: Primary 43;
Secondary 53

**Print ISBN: 978-0-8218-4580-6
Product Code: MMONO/135**

List Price: $115.00

Individual Member Price: $92.00

# Modern Spherical Functions

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*Masaru Takeuchi*

This book presents an exposition of spherical functions on compact symmetric spaces, from the viewpoint of Cartan-Selberg. Representation theory, invariant differential operators, and invariant integral operators play an important role in the exposition. The author treats compact symmetric pairs, spherical representations for compact symmetric pairs, the fundamental groups of compact symmetric spaces, and the radial part of an invariant differential operator. Also explored are the classical results for spheres and complex projective spaces and the relation between spherical functions and harmonic polynomials. This book is suitable as a graduate textbook.

#### Readership

Mathematicians familiar with the Fourier expansion of a function on the unit circle who would like to study how this fact is generalized to homogeneous spaces.