Spectral Theory of the Laplace Operator
In the present chapter we analyse the operation of the Laplace-Beltrami operator on its natural domain in the Hilbert space L 2 (Г\IH) of squareintegrable functions on Г\IH for discrete subgroups Г < PSL(2, ℂ) in the frame-work of Hilbert space theory. Our discussion uses certain well-known facts about self-adjoint operators on Hilbert spaces, they can be found in Dunford, Schwartz (1958), Reed, Simon (1972) or Kato (1976).
KeywordsLaplace Operator Spectral Theory Discrete Group Fundamental Domain Eisenstein Series
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