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Author Unterberger, Andrรฉ. author Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi [electronic resource] / by Andrรฉ Unterberger Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2003 http://dx.doi.org/10.1007/978-3-0348-7978-1 IX, 246 p. online resource

CONTENT

1 Introduction -- 1 Automorphic Distributions and the Weyl Calculus -- 2 he Weyl calculus, the upper half-plane, and automorphic distributions -- 3 Eisenstein distributions, Diracโ{128}{153}s comb and Bezoutโ{128}{153}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 -- 13 The Roelcke-Selberg expansion of functions associated with $$\mathfrak{E}_{{{{\nu }_{1}}}}̂{\sharp }\# \mathfrak{E}_{{\nu 2}}̂{\sharp }$$ the continuous part -- 14 The Roelcke-Selberg expansion of functions associated with $$\mathfrak{E}_{{{{\nu }_{1}}}}̂{\sharp }\# \mathfrak{E}_{{\nu 2}}̂{\sharp }$$ the discrete part -- 15 A proof of the main formula -- 16 Towards the completion of the multiplication table -- 4 Further Perspectives -- 17 Another way to compose Weyl symbols -- 18 Odd automorphic distributions and modular forms of non-zero weight -- 19 New perspectives and problems in quantization theory -- Index of Notation

Mathematics Topological groups Lie groups Global analysis (Mathematics) Manifolds (Mathematics) Operator theory Partial differential equations Number theory Quantum physics Mathematics Operator Theory Topological Groups Lie Groups Global Analysis and Analysis on Manifolds Partial Differential Equations Number Theory Quantum Physics

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