In this paper we develop the spectral theory of the Laplace-Beltrami operator for geometrically periodic hyperbolic 3-manifolds, [double-struck capital]H³/G. Using the theory of holomorphic families of operators, we obtain a quantitative description of the absolutely continuous …
We evaluate the Selberg trace formula for all discrete, irreducible, cofinite subgroups of PSL₂ ([double-struck capital]R)[italic superscript]n. In particular, this involves studying the spectral theory of the fundamental domain, and the analysis of the appropriate Eisenstein se…
"A complete treatment of the Feynman-Kac formula is given. The theory is applied to such topics as compactness or trace class properties of differences of Feynman-Kac semigroups, preservation of absolutely continuous and/or essential spectra and completeness of scattered systems…
This book emphasizes the geometric approach to the spectral analysis of linear partial differential operators on Hilbert space which exploits the local action of the operator. The geometric techniques are illustrated through examples from the theory of Schrödinger operators. The…
