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This volume contains the proceedings of the International Conference on "Par tial Differential Equations" held in HolzhaujErzgebirge, Germany, July 3~9, 1994. The conference was sponsored by the Max-Planck-Gesellschaft, the Deutsche For schungsgemeinschaft, the Land Brandenburg and the Freistaat Sachsen. It was initiated by the Max-Planck-Research Group "Partielle Differential gleichungen und Komplexe Analysis" at the University of Potsdam as one of the annual meetings of the research group. This conference is part of a series begun by the former Karl-Weierstraf3-Institute of Mathematics in Berlin, with the confer ences in Ludwigsfelde 1976, Reinhardsbrunn 1985, Holzhau 1988 (proceedings in the Teubner Texte zur Mathematik 112, Teubner-Verlag 1989), Breitenbrunn 1990 (proceedings in the Teubner Texte zur Mathematik 131, Teubner-Verlag 1992), and Lambrecht 1991 (proceedings in Operator Theory: Advances and Applications, Vol. 57, Birkhiiuser Verlag 1992); subsequent conferences took place in Potsdam in 1992 and 1993 under the auspices of the Max-Planck-Research Group "Partielle Differentialgleichungen und Komplexe Analysis" at the University of Potsdam. It was the intention of the organizers to bring together specialists from differ ent areas of modern analysis, geometry and mathematical physics to discuss not only recent progress in the respective disciplines but also to encourage interaction between these fields. The scientific advisory board of the Holzhau conference consisted of S. Al beverio (Bochum), L. Boutet de Monvel (Paris), M. Demuth (Clausthal), P. Gilkey (Eugene), B. Gramsch (Mainz), B. Helffer (Paris), S.T. Kuroda (Tokyo), B.-W. Schulze (Potsdam).
A remark on coercive forms and associated semigroups.- Domain perturbation for the first eigenvalue of the Dirichlet Schrödinger operator.- Geometric transition for a class of hyperbolic operators with double characteristics.- Multi-quasi-elliptic operators in ?n.- Real analogue of the Bergman kernel.- Attractors of non-autonomous evolution equations with translation-compact symbols.- Localization for 2-dimensional random Schrödinger operators with magnetic fields.- Some problems of calculus of variations in infinite dimensions.- Finite capacities in spectral theory.- Classical N-body scattering.- Quantum Fermi accelerators with pure-point quasi-spectrum.- On moments of negative eigenvalues of an elliptic operator.- Magnetic Lieb-Thirring inequalities and stochastic oscillatory integrals.- On the trace density in deformation quantization.- The stationary phase method with remainder estimate as dimension of the space goes to infinity.- The eta invariant, equivariant spin bordism, and metrics of positive scalar curvature.- Generalized Strichartz inequalities for the wave equation.- Around the transfer operator and the Totter-Kato formula.- Bands and gaps for periodic magnetic Hamiltonians.- H?-calculus for second order elliptic operators in divergence form.- Path integral for the relativistic Schrödinger semigroup.- Semiclassical spectral asymptotics and multiparticle quantum theory.- Product formulas and error estimates.- On inequalities for the bound states of Schrödinger operators.- Some examples of two-term spectral asymptotics for sets with fractal boundary.- Estimates for Fourier transforms of surface-carried densities on surfaces with singular points.- On adiabatic reduction theory.- Recurrence for fractional powers of diffusion operators in terms of volume-growth.- Band spectrum for Schrödinger operators with strong periodic magnetic fields.- Mellin pseudodifferential operators with operator symbols and its applications.- Hypoellipticity of certain differential operators with degeneration of infinite order.- On approximation of solutions of elliptic boundary value problems for Petrovskii elliptic systems by linear combinations of fundamental solutions.- The reduced wave operator with two unbounded media.- Mellin quantization in the cone calculus for Boutet de Monnvel’s algebra.- Transmission algebras on singular spaces with components of different dimensions.- On approximation by solutions of non-local elliptic problems.- A stability set in the Cauchy problem for elliptic systems.- Discrete spectrum asymptotics for the Schrödinger operator.- Convergence of Scbrödjnger operators on varying domains.- Localization for the Poisson model.- Systems of partial differential equations for a class of operator determinants.- Absorption semigroups, Feller property, and Kato class.- Gaussian estimates and analytic semigroups.- New channels of scattering for long-range potentials.- Participants.- Talks.