Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi

AvAndré Unterberger

Inbunden, Engelska, 2002

Del 209 i serien Progress in Mathematics

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2002-12-11
Mått:155 x 235 x 20 mm
Vikt:559 g
Format:Inbunden
Språk:Engelska
Serie:Progress in Mathematics
Antal sidor:246
Upplaga:2003
Förlag:Birkhauser Verlag AG
ISBN:9783764369095

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Innehållsförteckning

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.