Scattering theory for

twisted automorphic functions

Author:
Ralph Phillips

Journal:
Trans. Amer. Math. Soc. **350** (1998), 2753-2778

MSC (1991):
Primary 58G25, 11F72, 35L05

DOI:
https://doi.org/10.1090/S0002-9947-98-02164-3

MathSciNet review:
1466954

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Abstract: 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 with an irreducible unitary representation and satisfying . 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, and , for the solution operator. The scattering operator, which maps into , 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 is one, the elements of the scattering operator cannot vanish. However when this is no longer the case.

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Additional Information

**Ralph Phillips**

Affiliation:
Department of Mathematics, Stanford University, Stanford, California 94305

DOI:
https://doi.org/10.1090/S0002-9947-98-02164-3

Received by editor(s):
January 23, 1996

Article copyright:
© Copyright 1997
American Mathematical Society