On the Schwartz space isomorphism theorem for rank one symmetric space
نویسندگان
چکیده
منابع مشابه
On the Schwartz space isomorphism theorem for rank one symmetric space
Let X be a rank one Riemannian symmetric space of noncompact type. We recall that such a space can be realized as G/K, where G is a connected noncompact semisimple Lie group of real rank one with finite center and K is a maximal compact subgroup of G. Anker [2], in his paper gave a remarkably short and elegant proof of the Lp-Schwartz space isomorphism theorem for K bi-invariant functions on G ...
متن کاملOn the Schwartz Space of the Basic Affine Space
Let G be the group of points of a split reductive algebraic group G over a local field k and let X = G/U where U is the group of k-points of a maximal unipotent subgroup of G. In this paper we construct certain canonical G-invariant space S(X) (called the Schwartz space of X) of functions on X , which is an extension of the space of smooth compactly supported functions on X . We show that the s...
متن کاملInvariant distributions on a non-isotropic pseudo-Riemannian symmetric space of rank one
We investigate the structure of invariant distributions on a nonisotropic non-Riemannian symmetric space of rank one. Especially, the Jcriterion related to the generalized Gelfand pair is shown for this space without imposing the condition on the eigenfuction of the Laplace-Bertrami operator.
متن کاملBerezin-Toeplitz Quantization on the Schwartz Space of Bounded Symmetric Domains
Borthwick, Lesniewski and Upmeier [“Nonperturbative deformation quantization of Cartan domains,” J. Funct. Anal. 113 (1993), 153–176] proved that on any bounded symmetric domain (Hermitian symmetric space of non-compact type), for any compactly supported smooth functions f and g , the product of the Toeplitz operators TfTg on the standard weighted Bergman spaces can be asymptotically expanded i...
متن کاملA theorem on the Schwartz space of a reductive Lie group.
The purpose of this paper is to define the Fourier transform of an arbitrary tempered distribution on a reductive Lie group. To this end we define a topological vector space, [unk](G), in terms of the classes of irreducible unitary representations of G, which plays role of a dual Schwartz space. Our main theorem then asserts that the usual L(2) Fourier transform, when restricted to functions in...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings Mathematical Sciences
سال: 2007
ISSN: 0253-4142,0973-7685
DOI: 10.1007/s12044-007-0029-6