Pseudo-Differential Operators and Generalized Functions

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.

Preface.- U. Battisti, S. Coriasco and E. Schrohe: A Class of Fourier Integral Operators on Manifolds with Boundary.- C. Boiti and D. Jornet: The Problem of Iterates in Some Classes of Ultradifferentiable Functions.- C. Bouzar and M.T. Khalladi: On Asymptotically Almost Periodic Generalized Solutions of Differential Equations.- E. Cordero, F. Nicola and L. Rodino: Gabor Wave Packets and Evolution Operators.- H. Fredriksson: A Weighted Version of Wiener’s Lemma in p-normed Algebras for 0 < p = 1.- L. Galleani: Time-Frequency Initial Value Problems for Random MIMO Systems.- G. Garello and A. Morando: Microlocal Regularity of Besov Type for Solutions to Quasi-elliptic Nonlinear Partial Differential Equations.- T. Gramchev, A. Lecke, S. Pilipiovic and L. Rodino: Gelfand–Shilov Type Spaces Through Hermite Expansions.- T. Gramchev and G. Tranquilli: Cauchy Problem for Second-order Hyperbolic Equations for Shubin Pseudodifferential Operators.- G. Hörmann, S. Konjik and M. Kunzinger: A Regularization Approach to Non-smooth Symplectic Geometry.- S. Mincheva-Kaminska: Equivalent Conditions for Integrability of Distributions.- I. Kmit and L. Recke: Time-periodic Second-order Hyperbolic Equations: Fredholmness, Regularity, and Smooth Dependence.- S. Kostadinova, S. Pilipovic, K. Saneva and J. Vindas: The Ridgelet Transform and Quasiasymptotic Behavior of Distributions.- T. Levajkovic H. Mena: Equations Involving Malliavin Derivative:A Chaos Expansion Approach.- J.-A. Marti: Generalized and Classical Solutions to a Characteristic Cauchy Problem with Hörmander Hypotheses.- I.V. Melnikova and U.A. Alekseeva: On Generalized Solutions to Stochastic Systems.- C. Sämann and R. Steinbauer: Geodesic Completeness of Generalized Space-times.- J. Toft: Gabor Analysis for a Broad Class of Quasi-Banach Modulation Spaces.- K. Yoshino: Spectral Analysis of Daubechies Localization Operators.