**Fields Institute Communications**

Volume: 52;
2007;
414 pp;
Hardcover

MSC: Primary 35; 42; 47; 58; 65; 94;

Print ISBN: 978-0-8218-4276-8

Product Code: FIC/52

List Price: $130.00

Individual Member Price: $104.00

**Electronic ISBN: 978-1-4704-3086-3
Product Code: FIC/52.E**

List Price: $130.00

Individual Member Price: $104.00

# Pseudo-Differential Operators: Partial Differential Equations and Time-Frequency Analysis

Share this page *Edited by *
*Luigi Rodino; Bert-Wolfgang Schulze; M. W. Wong*

A co-publication of the AMS and Fields Institute

This volume is based on lectures given at the workshop on pseudo-differential operators held at the Fields Institute from December 11, 2006 to December 15, 2006. The two main themes of the workshop and hence this volume are partial differential equations and time-frequency analysis. The contents of this volume consist of five mini-courses for graduate students and post-docs, and fifteen papers on related topics. Of particular interest in this volume are the mathematical underpinnings, applications and ramifications of the relatively new Stockwell transform, which is a hybrid of the Gabor transform and the wavelet transform. The twenty papers in this volume reflect modern trends in the development of pseudo-differential operators.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Table of Contents

# Table of Contents

## Pseudo-Differential Operators: Partial Differential Equations and Time-Frequency Analysis

- Cover Cover11
- Half title page i2
- Title page iii4
- Contents v6
- Preface vii8
- On Hörmander operators and non-holonomic geometry 110
- Weyl transforms and the inverse of the sub-Laplacian on the Heisenberg group 2736
- Pseudo-differential calculus on manifolds with geometric singularities 3746
- Corner operators and applications to elliptic complexes 8594
- Ellipticity of a class of corner operators 131140
- Pseudodifferential methods for boundary value problems 171180
- Invertibility of parabolic Pseudodifferential operators 201210
- Semilinear pseudo-differential equations and travelling waves 213222
- Continuity and compactness properties of pseudo-differential operators 239248
- Trace ideals for Fourier integral operators with non-smooth symbols 255264
- Schatten-von Neumann norm inequalities for two-wavelet localization operators 265274
- Why use the S-transform? 279288
- Applying the S-transform to magnetic resonance imaging texture analysis 311320
- Inversion formulas for two-dimensional Stockwell transforms 323332
- Localization of signal and image features with the TT-transform 331340
- Weight functions in time-frequency analysis 343352
- Shannon type sampling theorems on the Heisenberg group 367376
- Rihaczek transforms and pseudo-differential operators 375384
- A unified point of view on time-frequency representations and pseudo-differential operators 383392
- Blind source separation using time-frequency analysis 401410
- Back Cover Back Cover1426

#### Readership

Graduate students and research mathematicians interested in pseudo-differential operators.

#### Reviews

I do not think it (is) an exaggeration to say that most of us who engage ourselves in study and research, will learn something of the present trends in pseudo-differential operators on just about every page. ... An equally outstanding feature of an outstanding volume apart from an excellent layout of mathematical equations, is the list of references appended to each paper.

-- Current Engineering Practice