منابع مشابه
Fourier Analysis on Semisimple Symmetric Spaces
A homogeneous space X = G/H of a connected Lie group G is called a symmetric homogeneous space if there exists an involution σ of G such that H lies between the fixed point group G and its identity component Go . Example 0. For a connected Lie group G′, put G = G′×G′, σ(g1, g2) ) = (g2, g1) and H = G. Then the homogeneous space X = G/H is naturally isomorphic to G′ by the map (g1, g2) 7→ g1g−1 ...
متن کاملThe Abel, Fourier and Radon transforms on symmetric spaces
In this paper we prove some recent results on the three transforms in the title and discuss their relationships to older results. The spaces we deal with are symmetric spaces X = G/K of the noncompact type, G being a connected noncompact semisimple Lie group with finite center and K a maximal compact subgroup. For the two natural Radon transforms on X we prove a new inversion formula and a shar...
متن کاملThe Fourier Transform on Symmetric Spaces and Applications 1. the Fourier Transform
The symmetric spaces the title refers to are the spaces X = G=K where G is a connected semisimple Lie group with nite center and K is a maximal compact subgroup. The Fourier transform on X is deened by means of the Iwasawa decomposition G = NAK of G where N is nilpotent and A abelian. Let g; n; a; k denote the corresponding Lie algebras. We also need the group M = K A ; the centralizer of A in ...
متن کاملGeneralized Symmetric Berwald Spaces
In this paper we study generalized symmetric Berwald spaces. We show that if a Berwald space $(M,F)$ admits a parallel $s-$structure then it is locally symmetric. For a complete Berwald space which admits a parallel s-structure we show that if the flag curvature of $(M,F)$ is everywhere nonzero, then $F$ is Riemannian.
متن کاملHarmonic Analysis on Real Reductive Symmetric Spaces
Let G be a reductive group in the Harish-Chandra class e.g. a connected semisimple Lie group with finite center, or the group of real points of a connected reductive algebraic group defined over R. Let σ be an involution of the Lie group G, H an open subgroup of the subgroup of fixed points of σ. One decomposes the elements of L(G/H) with the help of joint eigenfunctions under the algebra of le...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1951
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.37.8.529