Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations [recurso electrónico] : International Workshop, York University, Canada, August 4–8, 2008 / edited by Bert-Wolfgang Schulze, M. W. Wong.

Boundary Value Problems with the Transmission Property -- Spectral Invariance of SG Pseudo-Differential Operators on L p ? n -- Edge-Degenerate Families of Pseudo-Differential Operators on an Infinite Cylinder -- Global Regularity and Stability in S-Spaces for Classes of Degenerate Shubin Operators -- Weyl’s Lemma and Converse Mean Value for Dunkl Operators -- Dirichlet Problems for Inhomogeneous Complex Mixed-Partial Differential Equations of Higher order in the Unit Disc: New View -- Dirichlet Problems for the Generalized n-Poisson Equation -- Schwarz, Riemann, Riemann-Hilbert Problems and Their Connections in Polydomains -- L p -Boundedness of Multilinear Pseudo-Differential Operators -- A Trace Formula for Nuclear Operators on L p -- Products of Two-Wavelet Multipliers and Their Traces -- Pseudo-Differential Operators on ? -- Pseudo-Differential Operators with Symbols in Modulation Spaces -- Phase-Space Differential Equations for Modes -- Two-Window Spectrograms and Their Integrals -- Time-Time Distributions for Discrete Wavelet Transforms -- The Stockwell Transform in Studying the Dynamics of Brain Functions.

The International Workshop on Pseudo-Di?erential Operators: Complex Analysis and Partial Di?erential Equations was held at York University on August 4–8, 2008. The ?rst phase of the workshop on August 4–5 consisted of a mini-course on pseudo-di?erential operators and boundary value problems given by Professor Bert-Wolfgang Schulze of Universita ¨t Potsdam for graduate students and po- docs. This was followed on August 6–8 by a conference emphasizing boundary value problems;explicit formulas in complex analysis and partialdi?erential eq- tions; pseudo-di?erential operators and calculi; analysis on the Heisenberg group and sub-Riemannian geometry; and Fourier analysis with applications in ti- frequency analysis and imaging. The role of complex analysis in the development of pseudo-di?erential op- ators can best be seen in the context of the well-known Cauchy kernel and the related Poisson kernel in, respectively, the Cauchy integral formula and the Po- son integral formula in the complex plane C. These formulas are instrumental in solving boundary value problems for the Cauchy-Riemann operator? and the Laplacian?onspeci?cdomainswith theunit disk andits biholomorphiccomp- ion, i. e. , the upper half-plane, as paradigm models. The corresponding problems in several complex variables can be formulated in the context of the unit disk n n in C , which may be the unit polydisk or the unit ball in C .

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