Pseudo-Differential Operators: Analysis, Applications and Computations

This volume consists of eighteen peer-reviewed papers related to lectures on pseudo-differential operators presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at Imperial College London on July 13-18, 2009. Featured in this volume are the analysis, applications and computations of pseudo-differential operators in mathematics, physics and signal analysis. This volume is a useful complement to the volumes "Advances in Pseudo-Differential Operators", "Pseudo-Differential Operators and Related Topics", "Modern Trends in Pseudo-Differential Operators", "New Developments in Pseudo-Differential Operators" and "Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations" published in the same series in, respectively, 2004, 2006, 2007, 2009 and 2010.

Preface. - Adaptive Wavelet Computations for Inverses of Pseudo-Differential Operators. - Spectral Theory of Pseudo-Differential Operators on S1. - A Characterization of Compact Pseudo-Differential Operators on S1. - Melin Operator with Asymptotics on Manifolds with Corners. - The Iterative Structure of the Corner Calculus. - Elliptic Equations and Boundary Value Problems in Non-Smooth Domains. - Calculus of Pseudo-Differential Operators and a Local Index of Dirac Operators. - Lp Bounds for a Class of Fractional Powers of Subelliptic Operators. - The Heat Kernel and Green Function of the Generalized Hermite Operator, and the Abstract Cauchy Problem for the Abstract Hermite Operator. - Local Exponential Estimates for h-Pseudo-Differential Operators with Operator-Valued Symbols. - Global Solvability in Functional Spaces for Smooth Nonsingular Vector Fields in the Plane. - Fuchsian Mild Microfunctions with Fractional Order and their Applications to Hyperbolic Equations. - The Continuity of Solutions with respect to a Parameter to Symmetric Hyperbolic Systems. - Generalized Gevrey Ultradistributions and their Microlocal Analysis. - Weyl Rule and Pseudo-Differential Operators for Arbitrary Operators. - Time-Frequency Characterization of Stochastic Differential Equations. - Wigner Representation Associated with Linear Transformations of the Time-Frequency Plane. - Some Remarks on Localization Operators.