Pseudo-differential Operators: Partial Differential Equations and Time-frequency AnalysisLuigi Rodino, Bert-Wolfgang Schulze, Man Wah Wong American Mathematical Soc., 21 nov. 2007 - 414 pages 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. |
Table des matières
| 1 | |
Weyl Transforms and the Inverse of the SubLaplacian on the Heisenberg Group | 27 |
PseudoDifferential Calculus on Manifolds with Geometric Singularities | 37 |
Corner Operators and Applications to Elliptic Complexes | 85 |
Ellipticity of a Class of Corner Operators | 131 |
Pseudodifferential Methods for Boundary Value Problems | 171 |
Invertibility of Parabolic Pseudodifferential Operators | 201 |
Semilinear PseudoDifferential Equations and Travelling Waves | 213 |
Why Use the STransform? | 279 |
Applying the STransform to Magnetic Resonance Imaging Texture Analysis | 311 |
Inversion Formulas for TwoDimensional Stockwell Transforms | 323 |
Localization of Signal and Image Features with the TTTransform | 331 |
Weight Functions in TimeFrequency Analysis | 343 |
Shannon Type Sampling Theorems on the Heisenberg Group | 367 |
Rihaczek Transforms and PseudoDifferential Operators | 375 |
A Unified Point of View on TimeFrequency Representations and PseudoDifferential Operators | 383 |
Continuity and Compactness Properties of PseudoDifferential Operators | 239 |
Trace Ideals for Fourier Integral Operators with NonSmooth Symbols | 255 |
Schattenvon Neumann Norm Inequalities for TwoWavelet Localization Operators | 265 |
Blind Source Separation Using TimeFrequency Analysis | 401 |
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Expressions et termes fréquents
algebra amplitude analysis applied associated assume asymptotics Banach space belongs bounded calculus called classical closed compact complex components condition cone consider constant continuous corner corresponding defined Definition denote differential operators distribution edge elliptic equation estimate example exists extends Figure finite fixed formula Fourier transform Fredholm frequency function give given global implies integral introduce inverse isomorphism Lemma linear localization manifold Math Mathematics means Mellin Moreover norm Note obtain particular phase positive principal Proof properties Proposition proved pseudo-differential pseudodifferential operators References relation Remark representation respect result S-transform sampling satisfies Schulze sense shows signal singularities smooth Sobolev spaces solution spectrum symbol Theorem theory time-frequency variables wavelet weight window