Invariant function spaces on homogeneous manifolds of Lie groups and applications / M. L. Agranovskii ; A. I. Zaslavsky

Auteur principal : Agranovsky, Mark L'vovich, 1946-, AuteurAuteur secondaire : Zaslavsky, A. I., TraducteurType de document : MonographieCollection : Translations of mathematical monographs, 126Langue : anglais.Pays: Etats Unis.Éditeur : Providence : American Mathematical Society, 1993Description : 1 vol. (X- 131 p.) ; 26 cmISBN: 0821846043.ISSN: 0065-9282.Bibliographie : Bibliogr. p.127-131.Sujet MSC : 43A85, Abstract harmonic analysis, Harmonic analysis on homogeneous spaces
53C35, Global differential geometry, Differential geometry of symmetric spaces
32M15, Complex spaces with a group of automorphisms, Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
22E46, Lie groups, Semisimple Lie groups and their representations
43A90, Abstract harmonic analysis, Harmonic analysis and spherical functions
En-ligne : Zentralblatt | MathSciNet | AMS
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Bibliogr. p.127-131

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. (source : AMS)

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