André Unterberger

Pseudodifferential Operators with Automorphic Symbols (eBook, PDF)

• Format: PDF

Produktbeschreibung

The main results of this book combine pseudodifferential analysis with modular form and L-function theory, with the help of explicit spectral-theoretic calculations. The starting point is a notion of modular distribution in the plane, which will be new to most readers and which, under the Radon transformation, relates to the classical notion of non-holomorphic modular form. Holomorphic modular forms are also briefly considered, within a general scheme that addresses quantization theory and elementary but novel representation-theoretic concepts.

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Produktdetails

• Verlag: Springer Nature Switzerland
• Seitenzahl: 202
• Erscheinungstermin: 22. Juni 2015
• Englisch
• ISBN-13: 9783319186573
• Artikelnr.: 44127120

Inhaltsangabe

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.

Rezensionen

"The book under review is devoted to developing a satisfactory Weyl calculus on the class of tempered automorphic distributions under the group SL(2, Z). ... The book is ... readable and is an interesting introduction to the subject. The main ideas are explained in detail and illustrated by exact computations." ( Ng c Di p, Mathematical Reviews, December, 2015)