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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 |