Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi (Progress in Mathematics .209) (Softcover reprint of the original 1st ed. 2003. 2012. ix, 246 S. IX, 2)

Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2002.
The subject of this book is the study of automorphic distributions, by which is meant distributions on R 2 invariant under the linear action of SL(2,Z), and of the operators associated with such distributions under the Weyl rule of symbolic calculus.
Researchers and postgraduates interested in pseudodifferential analyis, the theory of non-holomorphic modular forms, and symbolic calculi will benefit from the clear exposition and new results and insights.
1 Introduction.- 1 Automorphic Distributions and the Weyl Calculus.- 2 he Weyl calculus, the upper half-plane, and automorphic distributions.- 3 Eisenstein distributions, Dirac s comb and Bezout s distribution.- 4 The structure of automorphic distributions.- 5 The main formula: a heuristic approach.- 2 A Higher-level Weyl Calculus of Operators.- 6 A tamer version of the Weyl calculus: the horocyclic calculus.- 7 The higher-level metaplectic representations.- 8 The radial parts of relativistic wave operators.- 9 The higher-level Weyl calculi.- 10 Can one compose two automorphic operators?.- 11 The sharp product of two power-functions: the Weyl case.- 12 Beyond the symplectic group.- 3 The Sharp Composition of Automorphic Distributions.- ...