Harmonic Analysis on Semisimple Symmetric Spaces a Survey of Some General Results
نویسنده
چکیده
We give a survey of the status of some of the fundamental problems in harmonic analysis on semisimple symmetric spaces, including the description of the discrete series, the deenition of the Fourier transform, the inversion formula, the Plancherel formula and the Paley{ Wiener theorem.
منابع مشابه
Spherical Analysis and Central Limit Theorems on Symmetric Spaces
We prove some results on the kernel of the Abel transform on an irreducible Riemannian symmetric space X = G=K with G noncompact and complex, in particular an estimate of this kernel. We also study the behaviour of spherical functions near the walls of Weyl chambers. We show how these harmonic spherical analysis results lead to a new proof of a central limit theorem of Guivarc'h and Raugi in th...
متن کاملPaley-wiener Theorem for Line Bundles over Compact Symmetric Spaces
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Chapter 2: Riemannian Symmetric Spaces and Related Structure Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
متن کاملThe classification problem for pseudo-Rie- mannian symmetric spaces
Riemannian and pseudo-Riemannian symmetric spaces with semisimple transvection group are known and classified for a long time. Contrary to that the description of pseudo-Riemannian symmetric spaces with non-semisimple transvection group is an open problem. In the last years some progress on this problem was achieved. In this article we want to explain these results and some of their applications.
متن کاملHarmonic Analysis on Homogeneous Spaces
This article is an expository paper. We first survey developments over the past three decades in the theory of harmonic analysis on reductive symmetric spaces. Next we deal with the particular homogeneous space of non-reductive type, the so called Siegel-Jacobi space that is important arithmetically and geometrically. We present some new results on the Siegel-Jacobi space.
متن کاملDeterminant Type Differential Operators on Homogeneous Siegel Domains
In harmonic analysis on classical domains of matrices, the differential operator whose symbol is the determinant polynomial plays important roles. Particularly, the operator is substantial in study of invariant Hilbert spaces of holomorphic functions on the domain [1, 2, 7, 14, 15, 21]. Considering the Siegel domain realization of a certain symmetric domain with Fourier-analytic methods, Jakobs...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997