Cuspidal discrete series for semisimple symmetric spaces

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 ...

The C-function for a Semisimple Symmetric Space 1 Spherical Functions for Riemannian Symmetric Spaces

We discuss the product formula for the c-function for a Riemannian symmetric space and the similar formula for a noncompactly causal symmetric space. We derive two functional equations between the c-functions using the product formulas. Finally some examples where the c-functions turn up in analysis on symmetric spaces are given. Let G be a connected semisimple Lie group with nite center. Let K...

Discrete Groups, Symmetric Spaces, and Global Holonomy

Nearly Holomorphic Functions and Relative Discrete Series of Weighted L-spaces on Bounded Symmetric Domains

Let Ω = G/K be a bounded symmetric domain in a complex vector space V with the Lebesgue measure dm(z) and the Bergman reproducing kernel h(z, w). Let dμα(z) = h(z, z̄) dm(z), α > −1, be the weighted measure on Ω. The group G acts unitarily on the space L(Ω, μα) via change of variables together with a multiplier. We consider the discrete parts, also called the relative discrete series, in the irr...

Institute for Mathematical Physics Nearly Holomorphic Functions and Relative Discrete Series of Weighted L 2 -spaces on Bounded Symmetric Domains Nearly Holomorphic Functions and Relative Discrete Series of Weighted L 2 -spaces on Bounded Symmetric Domains

Let = G=K be a bounded symmetric domain in a complex vector space V with the Lebesgue measure dm(z) and the Bergman reproducing kernel h(z; w) ?p. Let dd (z) = h(z; z) dm(z), > ?1, be the weighted measure on. The group G acts unitarily on the space L 2 ((;) via change of variables together with a multiplier. We consider the discrete parts, also called the relative discrete series, in the irredu...