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Pseudo-Differential Operators: Partial Differential Equations and Time-Frequency Analysis
Edited by: Luigi Rodino, Università di Torino, Italy, Bert-Wolfgang Schulze, Universität Potsdam, Germany, and M. W. Wong, York University, Toronto, ON, Canada
A co-publication of the AMS and Fields Institute.
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Fields Institute Communications
2007; 414 pp; hardcover
Volume: 52
ISBN-10: 0-8218-4276-5
ISBN-13: 978-0-8218-4276-8
List Price: US$123
Member Price: US$98.40
Order Code: FIC/52
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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).

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

Table of Contents

  • P. Greiner -- On Hörmander operators and non-holonomic geometry
  • A. Dasgupta and M. W. Wong -- Weyl transforms and the inverse of the sub-Laplacian on the Heisenberg group
  • B.-W. Schulze -- Pseudo-differential calculus on manifolds with geometric singularities
  • C.-I. Martin -- Corner operators and applications to elliptic complexes
  • N. Dines -- Ellipticity of a class of corner operators
  • C. L. Epstein -- Pseudodifferential methods for boundary value problems
  • V. Rabinovich -- Invertibility of parabolic Pseudodifferential operators
  • M. Cappiello, T. Gramchev, and L. Rodino -- Semilinear pseudo-differential equations and travelling waves
  • E. Buzano and J. Toft -- Continuity and compactness properties of pseudo-differential operators
  • F. Concetti and J. Toft -- Trace ideals for Fourier integral operators with non-smooth symbols
  • V. Catană -- Schatten-von Neumann norm inequalities for two-wavelet localization operators
  • R. G. Stockwell -- Why use the S-transform?
  • T. A. Bjarnason, S. Drabycz, D. H. Adler, J. G. Cairncross, and J. R. Mitchell -- Applying the S-transform to magnetic resonance imaging texture analysis
  • Y. Liu and M. W. Wong -- Inversion formulas for two-dimensional Stockwell transforms
  • C. R. Pinnegar -- Localization of signal and image features with the TT-transform
  • K. Gröchenig -- Weight functions in time-frequency analysis
  • R. R. Radha and S. Sivananthan -- Shannon type sampling theorems on the Heisenberg group
  • A. Mohammed and M. W. Wong -- Rihaczek transforms and pseudo-differential operators
  • P. Boggiatto, G. De Donno, and A. Oliaro -- A unified point of view on time-frequency representations and pseudo-differential operators
  • R. Ashino, T. Mandai, A. Morimoto, and F. Sasaki -- Blind source separation using time-frequency analysis
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