On the Structure of Operators with Automorphic Symbols
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
KeywordsAutomorphic distributions horocyclic calculus Berezin calculus
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