Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations

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 .

The expository paper on pseudo-differential operators and boundary value problems targeted at graduate students and post-docs is a focal point of the volume An emphasis is placed on explicit formulas in complex analysis for the first time Papers on applications and computations in time-frequency analysis are included Papers from experts in physical, engineering and medical sciences are presented Includes supplementary material: sn.pub/extras

Auteur
Bert-Wolfgang Schulze ist emeritierter Professor am Institut für Mathematik an der Universität Potsdam, Deutschland. Vor der politischen Wende war er Professor am Karl-Weierstrass-Institut in Berlin, 1984 Euler-Medaille der Akademie der Wisenschaften in Berlin. 1992-96 war er Leiter der Max-Planck-Arbeitsgruppe 'Partielle Differentialgleichungen und Komplexe Analysis' in Potsdam. Nach anfänglichem Studium in Geophysik erhielt er sein Universitätsdiplom in Mathematik in Leipzig 1968. Die Promotion zum Dr. rer.nat. 1970 und die Habilitation in Mathematik 1974 erfolgten an der Universität Rostock. Seine wissenschaftlichen Aktivitäten umfassen Potentialtheorie, Randwert-Probleme, pseudo-differentielle Algebren und Index-Theorie auf berandeten Mannigfaltgikeiten und Räumen mit Singularitäten, darunterTransmissions- und Riss Probleme, Asymptotik von Lösungen, Randwert-Theorie mit globalen Projektionsbedingungen.

Texte du rabat

This volume is an outgrowth of the international workshop entitled "Pseudo-Differential Operators: Complex Analysis and Partial Differential Equations" held at York University on August 4-8, 2009. It consists of the expository paper based on the 6-hour minicourse given by Professor Bert-Wolfgang Schulze, and sixteen papers based on lectures given at the workshop and on invitations. While the focus is on the current developments of pseudo-differential operators in the context of complex analysis and partial differential equations, other topics related to the analysis, applications and computations of pseudo-differential operators are featured. TOC:Contributions by B.-W. Schulze.- A. Dasgupta and M. W. Wong.- J. Abed and B.-W. Schulze.- T. Gramchev, S. Pilipovic and L. Rodino.- M. Maslouhi and R. Daher.- H. Begehr, Z. Du and N. Wang.- Ü. Aksoy and A. O. Celebi.- A. Mohammed.- V. Catana, S. Molahajloo and M. W. Wong.- J. Delgado.- V. Catana.- S. Molahajloo.- J. Toft.- L. Cohen.- P. Boggiatto, G. De Donno and A. Oliaro.- C. R. Pinnegar, H. Khosravani and P. Federico.- C. Liu, W. Gaetz and H. Zhu.

Contenu
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.