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Beschreibung
The main results of this book combine pseudo differential analysis with modular form theory. The methods rely for the most part on explicit spectral theory and the extended use of special functions. The starting point is a notion of modular distribution in the plane, which will be new to most readers and relates under the Radon transformation to the classical one of modular form of the non-holomorphic type. Modular forms of the holomorphic type are addressed too in a more concise way, within a general scheme dealing with quantization theory and elementary, but novel, representation-theoretic concepts.
The main results of this book combine pseudo differential analysis with modular form theory. The methods rely for the most part on explicit spectral theory and the extended use of special functions. The starting point is a notion of modular distribution in the plane, which will be new to most readers and relates under the Radon transformation to the classical one of modular form of the non-holomorphic type. Modular forms of the holomorphic type are addressed too in a more concise way, within a general scheme dealing with quantization theory and elementary, but novel, representation-theoretic concepts.
Zusammenfassung

Features a complete study of pseudodifferential operators with automorphic symbols

Covers a complete analysis of link between modular distributions (in the plane) and non-holomorphic modular forms in the half-plane

Includes an introduction to the case of holomorphic modular forms, linked to the new anaplectic representation and symbolic calculus

Includes supplementary material: [...]

Inhaltsverzeichnis
Introduction.- Basic modular distributions.- From the plane to the half-plane.- A short introduction to the Weyl calculus.- Composition of joint eigenfunctions of (...) and (...).- The sharp composition of modular distributions.- The operator with symbol (...).- from non-holomorphic to holomorphic modular forms.- Index.
Details
Erscheinungsjahr: 2015
Fachbereich: Analysis
Genre: Mathematik, Medizin, Naturwissenschaften, Technik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Pseudo-Differential Operators
Inhalt: x
202 S.
ISBN-13: 9783319186566
ISBN-10: 3319186566
Sprache: Englisch
Herstellernummer: 978-3-319-18656-6
Einband: Kartoniert / Broschiert
Autor: Unterberger, André
Hersteller: Birkhäuser
Pseudo-Differential Operators
Verantwortliche Person für die EU: Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße: 240 x 168 x 12 mm
Von/Mit: André Unterberger
Erscheinungsdatum: 26.06.2015
Gewicht: 0,371 kg
Artikel-ID: 104738421

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