Pseudo-Differential Operators: Groups, Geometry and Applications

Description

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. Front Matter....Pages i-viii Pseudo-Differential Operators on the Affine Group....Pages 1-14 Pseudo-differential Operators on Non-isotropic Heisenberg Groups with Multi-dimensional Centers....Pages 15-35 Curvature of the Heisenberg Group....Pages 37-46 Ellipticity with Global Projection Conditions....Pages 47-106 Multilinear Localization Operators Associated to Quaternion Fourier Transforms....Pages 107-118 A Time-Frequency Relationship Between the Langevin Equation and the Harmonic Oscillator....Pages 119-131 Are There Quantum Operators and Wave Functions in Standard Probability Theory....Pages 133-147 A Class of Non-Markovian Pseudo-differential Operators of Lévy Type....Pages 149-159 On the Solvability of Some Systems of Integro-Differential Equations with Anomalous Diffusion....Pages 161-179 Visualizing Discrete Complex-Valued Time-Frequency Representations....Pages 181-201 The Reassigned Spectrogram of the Stockwell Transform....Pages 203-218 Continuous Multiwavelet Transform for Blind Signal Separation....Pages 219-239