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Invariant Function Spaces on Homogeneous Manifolds of Lie Groups and Applications

Mark Lʹvovich Agranovskiĭ

出版	American Mathematical Society, 1993
主題	Mathematics / General
ISBN	08218460439780821846049
URL	http://books.google.com.hk/books?id=MzcyoAEACAAJ&hl=&source=gbs_api

註釋

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 nilpotent 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.