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The application by Fadeev and Pavlov of the Lax-Phillips scattering
theory to the automorphic wave equation led Professors Lax and
Phillips to reexamine this development within the framework of
their theory. This volume sets forth the results of that work in
the form of new or more straightforward treatments of the spectral
theory of the Laplace-Beltrami operator over fundamental domains of
finite area; the meromorphic character over the whole complex plane
of the Eisenstein series; and the Selberg trace formula. CONTENTS:
1. Introduction. 2. An abstract scattering theory. 3. A modified
theory for second order equations with an indefinite energy form.
4. The Laplace-Beltrami operator for the modular group. 5. The
automorphic wave equation. 6. Incoming and outgoing subspaces for
the automorphic wave equations. 7. The scattering matrix for the
automorphic wave equation. 8. The general case. 9. The Selberg
trace formula.
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