Pseudo-Differential Operators: Analysis, Applications and Computations

1. Front Matter

   Pages i-vii

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2. Adaptive Wavelet Computations for Inverses of Pseudo-Differential Operators

   • Qiang Guo, M. W. Wong

   Pages 1-14

3. Spectral Theory of Pseudo-Differential Operators on \(\mathbb{S}^1\)

   • Mohammad Pirhayati

   Pages 15-23

4. A Characterization of Compact Pseudo-Differential Operators on \(\mathbb{S}^1\)

   • Shahla Molahajloo

   Pages 25-29

5. Mellin Operators with Asymptotics on Manifolds with Corners

   • B.-W. Schulze, M. W. Wong

   Pages 31-78

6. The Iterative Structure of the Corner Calculus

   • B.-W. Schulze

   Pages 79-103

7. Elliptic Equations and Boundary Value Problems in Non-Smooth Domains

   • Vladimir B. Vasilyev

   Pages 105-121

8. Calculus of Pseudo-Differential Operators and a Local Index of Dirac Operators

   • Chisato Iwasaki

   Pages 123-136

9. L ^p Bounds for a Class of Fractional Powers of Subelliptic Operators

   • Julio Delgado

   Pages 137-154

10. The Heat Kernel and Green Function of the Generalized Hermite Operator, and the Abstract Cauchy Problem for the Abstract Hermite Operator

    • Viorel Catană

    Pages 155-171

11. Local Exponential Estimates for h-Pseudo-Differential Operators with Operator-Valued Symbols

    • V. S. Rabinovich

    Pages 173-190

12. Global Solvability in Functional Spaces for Smooth Nonsingular Vector Fields in the Plane

    • Roberto DeLeo, Todor Gramchev, Alexandre Kirilov

    Pages 191-210

13. Fuchsian Mild Microfunctions with Fractional Order and their Applications to Hyperbolic Equations

    • Yasuo Chiba

    Pages 211-218

14. The Continuity of Solutions with Respect to a Parameter to Symmetric Hyperbolic Systems

    • Wataru Ichinose

    Pages 219-234

15. Generalized Gevrey Ultradistributions and their Microlocal Analysis

    • Khaled Benmeriem, Chikh Bouzar

    Pages 235-250

16. Weyl Rule and Pseudo-Differential Operators for Arbitrary Operators

    • Leon Cohen

    Pages 251-264

17. Time-Frequency Characterization of Stochastic Differential Equations

    • Lorenzo Galleani

    Pages 265-274

18. Wigner Representations Associated with Linear Transformations of the Time-Frequency Plane

    • Paolo Boggiatto, Evanthia Carypis, Alessandro Oliaro

    Pages 275-288

19. Some Remarks on Localization Operators

    • Elena Cordero, Fabio Nicola

    Pages 289-305

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.

• electrical and computer engineering
• geometry
• operator theory
• partial differential equations
• quantum mechanics

• Dipto. Matematica, Università di Torino, Torino, Italy

  Luigi Rodino

• Department of Mathematics & Statistics, York University, Toronto, Canada

  M. W. Wong

• Dept. Mathematics & Statistics, York University, North York, Canada

  Hongmei Zhu

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