Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi [electronic resource]
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Author: Unterberger, André
Added by: sketch
Added Date: 2015-12-30
Language: eng
Subjects: Mathematics, Topological groups, Global analysis, Operator theory, Differential equations, Partial, Number theory, Quantum theory
Publishers: Basel : Birkhäuser Basel : Imprint : Birkhäuser
Collections: folkscanomy miscellaneous, folkscanomy, additional collections
ISBN Number: 9783034879781, 3034879784
Pages Count: 600
PPI Count: 600
PDF Count: 1
Total Size: 79.58 MB
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Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi
Author: André Unterberger
Published by Birkhäuser Basel
ISBN: 978-3-0348-9641-2
DOI: 10.1007/978-3-0348-7978-1
Table of Contents:
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 R2 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 -- 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
Author: André Unterberger
Published by Birkhäuser Basel
ISBN: 978-3-0348-9641-2
DOI: 10.1007/978-3-0348-7978-1
Table of Contents:
- Introduction
- Automorphic Distributions and the Weyl Calculus
- A Higher-level Weyl Calculus of Operators
- The Sharp Composition of Automorphic Distributions
- Further Perspectives
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 R2 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 -- 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
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