Pseudo-Differential Operators: Groups, Geometry and Applications

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M. W. Wong, Hongmei Zhu
Birkhäuser, Jan 20, 2017 - Mathematics - 239 pages

This volume consists of papers inspired by the special session on pseudo-differential operators at the 10th ISAAC Congress held at the University of Macau, August 3-8, 2015 and the mini-symposium on pseudo-differential operators in industries and technologies at the 8th ICIAM held at the National Convention Center in Beijing, August 10-14, 2015.

The twelve papers included present cutting-edge trends in pseudo-differential operators and applications from the perspectives of Lie groups (Chapters 1-2), geometry (Chapters 3-5) and applications (Chapters 6-12). Many contributions cover applications in probability, differential equations and time-frequency analysis. A focus on the synergies of pseudo-differential operators with applications, especially real-life applications, enhances understanding of the analysis and the usefulness of these operators.

 

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Contents

PseudoDifferential Operators on the Affine Group
1
Pseudodifferential Operators on Nonisotropic Heisenberg Groups with Multidimensional Centers
15
Curvature of the Heisenberg Group
37
Ellipticity with Global Projection Conditions
47
Multilinear Localization Operators Associated to Quaternion Fourier Transforms
107
A TimeFrequency Relationship Between the Langevin Equation and the Harmonic Oscillator
119
Are There Quantum Operators and Wave Functions in Standard Probability Theory
132
A Class of NonMarkovian Pseudodifferential Operators of Lévy Type
149
On the Solvability of Some Systems of IntegroDifferential Equations with Anomalous Diffusion
160
Visualizing Discrete ComplexValued TimeFrequencyRepresentations
181
The Reassigned Spectrogram of the Stockwell Transform
202
Continuous Multiwavelet Transform for Blind Signal Separation
219
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