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Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi

André Unterberger (Autor)

Buch | Hardcover

IX, 246 Seiten

2002
Springer Basel (Verlag)
978-3-7643-6909-5 (ISBN)

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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 R²invariant 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.

Erscheint lt. Verlag	11.12.2002
Reihe/Serie	Progress in Mathematics
Zusatzinfo	IX, 246 p.
Verlagsort	Basel
Sprache	englisch
Maße	155 x 235 mm
Gewicht	566 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	automorphic distribution • Calc • Calculus • DEX • Dirac • Distribution • Form • Function • Functions • Group • modular form • multiplication • operator theory • Partial differential equations • Proof • Sharp • Verteilung (math.)
ISBN-10	3-7643-6909-4 / 3764369094
ISBN-13	978-3-7643-6909-5 / 9783764369095
Zustand	Neuware