Pseudodifferential Operators with Automorphic Symbols

Başlık:

Yazar:

Unterberger, André. author.

ISBN:

9783319186573

Ek Yazar:

Unterberger, André. author.

Fiziksel Tanım:

X, 202 p. online resource.

Series:

Pseudo-Differential Operators, Theory and Applications, 11

Contents:

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.

Abstract:

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.

Konu Terimleri:

Mathematics.

Operator theory.

Number theory.

Added Corporate Author:

SpringerLink (Online service)

Electronic Access:

http://dx.doi.org/10.1007/978-3-319-18657-3

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Library	Materyal Türü	Barkod	Yer Numarası	Durum
Searching... Pamukkale Merkez Kütüphanesi	E-Kitap	79996-1001	QA329 -329.9	Searching... Unknown

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Özet

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.