Invariant Function Spaces on Homogenous Manifolds of Lie Groups and Applications
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A01=American Mathematical Society
Author_American Mathematical Society
Category=PBG
Category=PBKF
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Product details
- ISBN 9780821846049
- Weight: 482g
- Publication Date: 30 Aug 1993
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Hardback
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This book studies translation-invariant function spaces and algebras on homogeneous manifolds. The central topic is the relationship between the homogeneous structure of a manifold and the class of translation-invariant function spaces and algebras on the manifold. Agranovskii obtains classifications of translation-invariant spaces and algebras of functions on semisimple and milpotent Lie groups, Riemann symmetric spaces, and bounded symmetric domains. When such classifications are possible, they lead in many cases to new characterizations of the classical function spaces, from the point of view of their group of admissible changes of variable. The algebra of holomorphic functions plays an essential role in these classifications when a homogeneous complex or $CR$-structure exists on the manifold. This leads to new characterizations of holomorphic functions and their boundary values for one- and multidimensional complex domains.
