New Developments in Pseudo-differential Operators

This volume consists of seventeen 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 the Middle East Technical University in Ankara,Turkey on August 13-18, 2007, and invited papers by experts in the field. Included in this volume are such topics as analysis and partial differential equations related to the Heisenberg group; global analysis and pseudo-differential analysis on non-compact manifolds and manifolds with singularities; Fourier integral operators and Colombeau algebras with applications to partial differential equations; exotic pseudo-differential operators and regularity results on quasi-elliptic operators and hypoelliptic operators; Stockwell transforms in time-frequency analysis; and pseudo-differential operators on Lie groups with related results to sampling. This volume is a useful complement to the volumes 'œAdvances in Pseudo-Differential Operators'�, 'œPseudo-Differential Operators and Related Topics'� and 'œModern Trends in Pseudo-Differential Operators'� published in the same series in, respectively, 2004, 2006 and 2007.

Phase-space Weyl calculus and global hypoellipticity of a class of degenerate elliptic partial differential operators.- On classes of degenerate elliptic operators in Gelfand-Shilov spaces.- Weyl transforms and the heat equation for the sub-Laplacian on the Heisenberg group.- Construction of the fundamental solution and curvature of manifolds with boundary.- Operators with corner-degenerate symbols.- Ellipticity of Fredholm pseudo-differential operators on Lp(Rn).- Hyperbolic systems with discontinuous coefficients: generalized wavefront sets.- Generalized fourier integral operators on spaces of Colombeau type.- On local and global regularity of Fourier integral operators.- Type 1,1-operators defined by vanishing frequency modulation.- Regularity for quasi-elliptic pseudo-differential operators with symbols in Hölder classes.- Multi-anisotropic Gevrey regularity of hypoelliptic operators.- Modified Stockwell transforms and time-frequency analysis.- Localization operators for two-dimensional Stockwell transforms.- Pseudo-differential operators on S1.- On pseudo-differential operators on the group Su(2).- Sampling and pseudo-differential operators.