Spectral Theory of the Laplace Operator

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


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).


Laplace Operator Spectral Theory Discrete Group Fundamental Domain Eisenstein Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations