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

Edited by: Luigi Rodino Università di Torino, Torino, Italy
Bert-Wolfgang Schulze Universität Potsdam, Potsdam, Germany
M. W. Wong York University, Toronto, ON, Canada
A co-publication of the AMS and Fields Institute
Available Formats:
Hardcover ISBN: 978-0-8218-4276-8
Product Code: FIC/52
414 pp
List Price: $138.00 MAA Member Price:$124.20
AMS Member Price: $110.40 Electronic ISBN: 978-1-4704-3086-3 Product Code: FIC/52.E 414 pp List Price:$130.00
MAA Member Price: $117.00 AMS Member Price:$104.00
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List Price: $207.00 MAA Member Price:$186.30
AMS Member Price: $165.60 Click above image for expanded view Pseudo-Differential Operators: Partial Differential Equations and Time-Frequency Analysis Edited by: Luigi Rodino Università di Torino, Torino, Italy Bert-Wolfgang Schulze Universität Potsdam, Potsdam, Germany M. W. Wong York University, Toronto, ON, Canada A co-publication of the AMS and Fields Institute Available Formats:  Hardcover ISBN: 978-0-8218-4276-8 Product Code: FIC/52 414 pp  List Price:$138.00 MAA Member Price: $124.20 AMS Member Price:$110.40
 Electronic ISBN: 978-1-4704-3086-3 Product Code: FIC/52.E 414 pp
 List Price: $130.00 MAA Member Price:$117.00 AMS Member Price: $104.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$207.00
MAA Member Price: $186.30 AMS Member Price:$165.60
• Book Details

Fields Institute Communications
Volume: 522007
MSC: Primary 35; 42; 47; 58; 65; 94;

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.

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

• Chapters
• Peter Greiner - On Hörmander operators and non-holonomic geometry
• Aparajita Dasgupta and M. Wong - Weyl transforms and the inverse of the sub-Laplacian on the Heisenberg group
• Bert-Wolfgang Schulze - Pseudo-differential calculus on manifolds with geometric singularities
• C. Martin - Corner operators and applications to elliptic complexes
• N. Dines - Ellipticity of a class of corner operators
• Charles Epstein - Pseudodifferential methods for boundary value problems
• V. Rabinovich - Invertibility of parabolic Pseudodifferential operators
• Marco Cappiello, Todor Gramchev and Luigi Rodino - Semilinear pseudo-differential equations and travelling waves
• Ernesto Buzano and Joachim Toft - Continuity and compactness properties of pseudo-differential operators
• Francesco Concetti and Joachim Toft - Trace ideals for Fourier integral operators with non-smooth symbols
• Viorel Catană - Schatten-von Neumann norm inequalities for two-wavelet localization operators
• R. Stockwell - Why use the S-transform?
• Thorarin Bjarnason, Sylvia Drabycz, Daniel Adler, J. Cairncross and J. Mitchell - Applying the S-transform to magnetic resonance imaging texture analysis
• Yu Liu and M. Wong - Inversion formulas for two-dimensional Stockwell transforms
• C. Pinnegar - Localization of signal and image features with the TT-transform
• Karlheinz Gröchenig - Weight functions in time-frequency analysis
• R Radha and S. Sivananthan - Shannon type sampling theorems on the Heisenberg group
• Alip Mohammed and M. Wong - Rihaczek transforms and pseudo-differential operators
• Paolo Boggiatto, Giuseppe De Donno and Alessandro Oliaro - A unified point of view on time-frequency representations and pseudo-differential operators
• Ryuichi Ashino, Takeshi Mandai, Akira Morimoto and Fumio Sasaki - Blind source separation using time-frequency analysis
• 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
• Request Review Copy
Volume: 522007
MSC: Primary 35; 42; 47; 58; 65; 94;

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.

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

• Chapters
• Peter Greiner - On Hörmander operators and non-holonomic geometry
• Aparajita Dasgupta and M. Wong - Weyl transforms and the inverse of the sub-Laplacian on the Heisenberg group
• Bert-Wolfgang Schulze - Pseudo-differential calculus on manifolds with geometric singularities
• C. Martin - Corner operators and applications to elliptic complexes
• N. Dines - Ellipticity of a class of corner operators
• Charles Epstein - Pseudodifferential methods for boundary value problems
• V. Rabinovich - Invertibility of parabolic Pseudodifferential operators
• Marco Cappiello, Todor Gramchev and Luigi Rodino - Semilinear pseudo-differential equations and travelling waves
• Ernesto Buzano and Joachim Toft - Continuity and compactness properties of pseudo-differential operators
• Francesco Concetti and Joachim Toft - Trace ideals for Fourier integral operators with non-smooth symbols
• Viorel Catană - Schatten-von Neumann norm inequalities for two-wavelet localization operators
• R. Stockwell - Why use the S-transform?
• Thorarin Bjarnason, Sylvia Drabycz, Daniel Adler, J. Cairncross and J. Mitchell - Applying the S-transform to magnetic resonance imaging texture analysis
• Yu Liu and M. Wong - Inversion formulas for two-dimensional Stockwell transforms
• C. Pinnegar - Localization of signal and image features with the TT-transform
• Karlheinz Gröchenig - Weight functions in time-frequency analysis
• R Radha and S. Sivananthan - Shannon type sampling theorems on the Heisenberg group
• Alip Mohammed and M. Wong - Rihaczek transforms and pseudo-differential operators
• Paolo Boggiatto, Giuseppe De Donno and Alessandro Oliaro - A unified point of view on time-frequency representations and pseudo-differential operators
• Ryuichi Ashino, Takeshi Mandai, Akira Morimoto and Fumio Sasaki - Blind source separation using time-frequency analysis
• 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
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