New Developments in Pseudo-Differential Operators: ISAAC Group in Pseudo-Differential Operators (IGPDO), Middle East Technical University, Ankara, Turkey, August 2007

✍ Scribed by Maurice de Gosson (auth.), Luigi Rodino, M. W. Wong (eds.)

• Publisher: Birkhäuser Basel
• Year: 2009
• Tongue: English
• Leaves: 336
• Series: Operator Theory: Advances and Applications 189
• Edition: 1
• Category: Library

✦ Synopsis

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 “Advances in Pseudo-Differential Operators”, “Pseudo-Differential Operators and Related Topics” and “Modern Trends in Pseudo-Differential Operators” published in the same series in, respectively, 2004, 2006 and 2007.

✦ Table of Contents

Front Matter....Pages i-viii
Phase-Space Weyl Calculus and Global Hypoellipticity of a Class of Degenerate Elliptic Partial Differential Operators....Pages 1-14
Classes of Degenerate Elliptic Operators in Gelfand-Shilov Spaces....Pages 15-31
Weyl Transforms and the Heat Equation for the Sub-Laplacian on the Heisenberg Group....Pages 33-42
Construction of the Fundamental Solution and Curvature of Manifolds with Boundary....Pages 43-65
Operators with Corner-Degenerate Symbols....Pages 67-106
Ellipticity of Fredholm Pseudo-Differential Operators on L p (ℝ n )....Pages 107-116
Hyperbolic Systems with Discontinuous Coefficients: Generalized Wavefront Sets....Pages 117-136
Generalized Fourier Integral Operators on Spaces of Colombeau Type....Pages 137-184
On Local and Global Regularity of Fourier Integral Operators....Pages 185-200
Type 1,1-Operators Defined by Vanishing Frequency Modulation....Pages 201-246
Regularity for Quasi-Elliptic Pseudo-Differential Operators with Symbols in Hölder Classes....Pages 247-264
Multi-Anisotropic Gevrey Regularity of Hypoelliptic Operators....Pages 265-273
Modified Stockwell Transforms and Time-Frequency Analysis....Pages 275-285
Localization Operators for Two-Dimensional Stockwell Transforms....Pages 287-296
Pseudo-Differential Operators on $$ \mathbb{S}^1 $$ ....Pages 297-306
On Pseudo-Differential Operators on Group SU(2)....Pages 307-322
Sampling and Pseudo-Differential Operators....Pages 323-332

✦ Subjects

Operator Theory; Partial Differential Equations; Global Analysis and Analysis on Manifolds