Automorphic Pseudodifferential Analysis and Higher Level Weyl Calculi

von André Unterberger

260 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Progress in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Mathematische Analysis, allgemein Differentialrechnung und -gleichungen
• ISBN: 9783034896412
• Sprache: Englisch
• Erscheinungsdatum: 24.10.2012
• Größe: 235 x 155 mm
• Verlag: Birkhäuser