Scattering theory for twisted automorphic functions

作     者：Phillips, R 

作者机构：Stanford Univ Dept Math Stanford CA 94305 USA 

出 版 物：《TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY》 (美国数学会汇刊)

年 卷 期：1998年第350卷第7期

页      面：2753-2778页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：.Scattering Theory Eisenstein series automorphic functions spectral representation constant term translation representations commutes with translation 

摘      要：The purpose of this paper is to develop a scattering theory for twisted automorphic functions on the hyperbolic plane, defined by a cofinite (but not cocompact) discrete group Gamma with an irreducible unitary representation rho and satisfying u(gamma z) = rho(gamma)u(z). The Lax-Phillips approach is used with the wave equation playing a central role. Incoming and outgoing subspaces are employed to obtain corresponding unitary translation representations, R- and R+, for the solution operator. The scattering operator, which maps R(-)f into R(+)f, is unitary and commutes with translation. The spectral representation of the scattering operator is a multiplicative operator, which can be expressed in terms of the constant term of the Eisenstein Series. When the dimension of rho is one, the elements of the scattering operator cannot vanish. However when dim(rho) 1 this is no longer the case.