Pseudo-Differential Operators: Analysis, Applications and Computations

Based on the ISAAC Group in Pseudo-Differential Operators (IGPDO) held at Imperial College London, this volume provides pseudo-differential operators. Topics include the analysis, applications and computations of pseudo-differential operators in mathematics.

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.

Most new developments in pseudo-differential operators are represented Numerical computations of pseudo-differential operators and discrete analogs of pseudo-differential operators are featured Diversity of topics related to pseudo-differential operators is presented Includes supplementary material: sn.pub/extras

Inhalt

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.