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Pseudo Casimir operator

  • Roelof W. Bruggeman
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

In this chapter we consider — in a more general context the operator α A discussed in 1.6.2, and its resolvent. We call a A the pseudo Casimir operator, as it is the generalization of the pseudo Laplacian of Colin de Verdière, [12]. We use the resolvent to prove a central result of this book, Theorem 9.4.1. This theorem gives the existence of meromorphic families of automorphic forms that satisfy certain conditions on their Fourier terms. The theorem implies that — generically on an open neighborhood in v × ℂ of any point in v r x ℂ there are as many families of automorphic forms as the Maass-Selberg relation allows, see Section 9.5. In the context of Section 1.6, Theorem 9.4.1 amounts to the construction of \(^a\widetilde E\) (r, s) in 1.6.4.

Keywords

Eisenstein Series Automorphic Form Selfadjoint Operator Casimir Operator Selfadjoint Extension 
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.

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Copyright information

© Springer Basel AG 1994

Authors and Affiliations

  • Roelof W. Bruggeman
    • 1
  1. 1.Mathematisch InstituutUniversiteit UtrechtUtrechtThe Netherland

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