Invertible functions on nonarchimedean symmetric spaces

Functions on Symmetric Spaces and Oscillator Representation

In this paper, we study the L functions on U(2n)/O(2n) and Mp(n,R). We relate them using the oscillator representation. We first study some isometries between various L spaces using the compactification we defined in [6]. These isometries were first introduced by Betten-Ólafsson in [3] . We then give a description of the matrix coefficients of the oscillator representation ω in terms of algebra...

Left invertible semigroups on Hilbert spaces . ∗

For strongly continuous semigroups on a Hilbert space, we present a short proof of the fact that the left-inverse of a left-invertible semigroup can be chosen to be a semigroup as well. Furthermore, we show that this semigroup need not to be unique.

Geometric zeta-functions of locally symmetric spaces

The theory of geometric zeta functions for locally symmetric spaces as initialized by Selberg and continued by numerous mathematicians is generalized to the case of higher rank spaces. We show analytic continuation, describe the divisor in terms of tangential cohomology and in terms of group cohomology which generalizes the Patterson conjecture. We also extend the range of zeta functions in con...

Polynomial estimates for c-functions on reductive symmetric spaces

The c-functions, related to a reductive symmetric space G/H and a fixed representation τ of a maximal compact subgroup K of G, are shown to satisfy polynomial bounds in imaginary directions.

A Fatou-type Theorem for Harmonic Functions on Symmetric Spaces