Bert-Wolfgang Schulze Book order

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 ."

In the book, new methods in the theory of differential equations on manifolds with singularities are presented. The semiclassical theory in quantum mechanics is employed, adapted to operators that are degenerate in a typical way. The degeneracies may be induced by singular geometries, e.g., conical or cuspidal ones. A large variety of non-standard degenerate operators are also discussed.The semiclassical approach yields new results and unexpected effects, also in classical situations. For instance, full asymptotic expansions for cuspidal singularities are constructed, and nonstationary problems on singular manifolds are treated. Moreover, finiteness theorems are obtained by using operator algebra methods in a unified framework. Finally the method of characteristics for general elliptic equations on manifolds with singularities is developed in the book.