Invariant function spaces on homogeneous manifolds of Lie groups and applications
著者
書誌事項
Invariant function spaces on homogeneous manifolds of Lie groups and applications
（Translations of mathematical monographs, v. 126）
American Mathematical Society, c1993
- タイトル別名
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Инвариантные пространства функций на однородных многообразиях групп ли и их приложения
Invariantnye prostranstva funkt︠s︡iĭ na odnorodnykh mnogoobrazii︠a︡kh grupp li i ikh prilozhenii︠a︡
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注記
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
Function spaces and function algebras on differentiable manifolds and symmetric spaces of noncompact type Translation invariant function spaces and function algebras on noncompact Lie groups Mobius spaces and algebras on symmetric domains and their Shilov boundaries Holomorphy tests in symmetric domains involving the automorphism group. Related problems References.
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