Pseudo-differential operators : partial differential equations and time-frequency analysis


Pseudo-differential operators : partial differential equations and time-frequency analysis

Luigi Rodino, Bert-Wolfgang Schulze, M.W. Wong, editors

(Fields Institute communications, v. 52)

American Mathematical Society , Fields Institute for Research in Mathematical Sciences, c2007

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Includes bibliographical references



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.


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

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