Pseudodifferential Operators with Automorphic Symbols

✍ Scribed by André Unterberger (auth.)

• Publisher: Birkhäuser Basel
• Year: 2015
• Tongue: English
• Leaves: 208
• Series: Pseudo-Differential Operators 11
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvi
Basic modular distributions....Pages 7-26
From the plane to the half-plane....Pages 27-49
A short introduction to the Weyl calculus....Pages 51-81
Composition of joint eigenfunctions of (\varepsilon\; \mathrm{and}\ \xi\frac{\partial}{\partial x}) ....Pages 83-122
The sharp composition of modular distributions....Pages 123-167
The operator with symbol (\mathfrak{E}_{\upsilon}) ....Pages 169-182
From non-holomorphic to holomorphic modular forms....Pages 183-195
Back Matter....Pages 197-202

✦ Subjects

Operator Theory; Number Theory