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Spectral Theory of the Laplace Operator

  • Jürgen Elstrodt
  • Fritz Grunewald
  • Jens Mennicke
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

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).

Keywords

Laplace Operator Spectral Theory Discrete Group Fundamental Domain Eisenstein Series 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Jürgen Elstrodt
    • 1
  • Fritz Grunewald
    • 2
  • Jens Mennicke
    • 3
  1. 1.Mathematisches InstitutUniversität MünsterMünsterGermany
  2. 2.Mathematisches InstitutUniversität DüsseldorfDüsseldorfGermany
  3. 3.Fakultät für MathematikUniversität BielefeldBielefeldGermany

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