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On the Structure of Operators with Automorphic Symbols

  • André Unterberger
Part of the Operator Theory: Advances and Applications book series (OT, volume 210)

Abstract

We consider automorphic distributions on ℝ2, a concept slightly more precise than that of automorphic functions on the hyperbolic half-plane: these objects introduce themselves in a natural way in symbolic calculi of operators such as Weyl’s or the horocyclic calculus, linked to the projective discrete series of SL(2, ℝ). We interpret in operator- theoretic terms various constructions of number-theoretic interest, some of which raise quite deep questions.

Mathematics Subject Classification (2000)

11F11 11F27 47G30 

Keywords

Automorphic distributions horocyclic calculus Berezin calculus 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • André Unterberger
    • 1
  1. 1.Mathématiques (FRE 3111)Université de ReimsREIMS Cedex 2France

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