Pseudo-Differential Operators and Generalized Functions

✍ Scribed by Stevan Pilipović, Joachim Toft (eds.)

• Publisher: Birkhäuser Basel
• Year: 2015
• Tongue: English
• Leaves: 288
• Series: Operator Theory: Advances and Applications 245
• Edition: 1
• Category: Library

✦ Synopsis

This book gathers peer-reviewed contributions representing modern trends in the theory of generalized functions and pseudo-differential operators. It is dedicated to Professor Michael Oberguggenberger (Innsbruck University, Austria) in honour of his 60th birthday. The topics covered were suggested by the ISAAC Group in Generalized Functions (GF) and the ISAAC Group in Pseudo-Differential Operators (IGPDO), which met at the 9th ISAAC congress in Krakow, Poland in August 2013. Topics include Columbeau algebras, ultra-distributions, partial differential equations, micro-local analysis, harmonic analysis, global analysis, geometry, quantization, mathematical physics, and time-frequency analysis. Featuring both essays and research articles, the book will be of great interest to graduate students and researchers working in analysis, PDE and mathematical physics, while also offering a valuable complement to the volumes on this topic previously published in the OT series.

✦ Table of Contents

Front Matter....Pages i-viii
A Class of Fourier Integral Operators on Manifolds with Boundary....Pages 1-19
The Problem of Iterates in Some Classes of Ultradifferentiable Functions....Pages 21-33
On Asymptotically Almost Periodic Generalized Solutions of Differential Equations....Pages 35-43
Gabor Wave Packets and Evolution Operators....Pages 45-59
A Weighted Version of Wiener’s Lemma in p-normed Algebras for 0 < p ≤ 1....Pages 61-66
Time-Frequency Initial Value Problems for Random MIMO Systems....Pages 67-78
Microlocal Regularity of Besov Type for Solutions to Quasi-elliptic Nonlinear Partial Differential Equations....Pages 79-94
Gelfand–Shilov Type Spaces Through Hermite Expansions....Pages 95-105
Cauchy Problem for Second-order Hyperbolic Equations for Shubin Pseudodifferential Operators....Pages 107-118
A Regularization Approach to Non-smooth Symplectic Geometry....Pages 119-132
Equivalent Conditions for Integrability of Distributions....Pages 133-147
Time-periodic Second-order Hyperbolic Equations: Fredholmness, Regularity, and Smooth Dependence....Pages 149-183
The Ridgelet Transform and Quasiasymptotic Behavior of Distributions....Pages 185-197
Equations Involving Malliavin Derivative: A Chaos Expansion Approach....Pages 199-216
Generalized and Classical Solutions to a Characteristic Cauchy Problem with Hörmander Hypotheses....Pages 217-229
On Generalized Solutions to Stochastic Systems....Pages 231-241
Geodesic Completeness of Generalized Space-times....Pages 243-253
Gabor Analysis for a Broad Class of Quasi-Banach Modulation Spaces....Pages 255-284
Spectral Analysis of Daubechies Localization Operators....Pages 285-290

✦ Subjects

Topological Groups, Lie Groups; Several Complex Variables and Analytic Spaces; Partial Differential Equations; Operator Theory; Abstract Harmonic Analysis; Functional Analysis