Boundary Value Problems and Singular Pseudo-differential Operators covers the analysis of pseudo-differential operators on manifolds with conical points and edges. The standard singular integral operators on the half-axis as well as boundary value problems on smooth manifolds are treated as particular cone and wedge theories. Particular features of the book are:
* A self-contained presentation of the cone pseudo-differential calculus
* A general method for pseudo-differential analysis on manifolds with edges for arbitrary model cones in spaces with discrete and continuous asymptoties
* The presentation of the algebra of boundary value problems with the transmission property, obtained as a modification of the general wedge theory
* A new exposition of the pseudo-differential calculus with operator-valued symbols, based on twisted homogeneity as well as on parameter-dependent theories and reductions of orders.
The coverage of this book helps to enrich the general theory of partial differential equations, thus making it essential reading for researchers and practitioners in mathematics, physics and the applied sciences. Contents: Preface Pseudo-differential operators Mellin pseudo-differential operators on manifolds with conical singularities Pseudo-differential calculus on manifolds with edges Boundary value problems Bibliography Index

This volume contains the proceedings of the international conference on " Operator Calculus and Spectral Theory" in Lambrecht, Germany, Decem- ber 9. - 14. , 1991, sponsored by the Deutsche Forschungsgemeinschaft, and by the Karl-Weierstrass-Institute of Mathematics, Berlin. The idea was to bring together specialists from different areas of modern analysis, geometry and mathematical physics, in a similar spirit as in the earlier series of conferences of the Karl-Weierstrass- Institute (Ludwigsfelde, 1976; Reinhardsbrunn, 1985; Holzhau, 1988; Breitenbrunn,1990). Berlin, Mainz M. Demuth B. Gramsch B. -W. Schulze List of talks given in La. brecht. 8. - 14. December 91 Name Title S. Albeverio Some recent deveiopments in Dirichlet forms and associated processes U. Bunke On the spectral flow of Dirac operators with negative definite functions as symbols - applications in probability theory and mathematical physics M. Combescure Recurrent versus diffusive behaviour for time-dependent quantum Hamiltonian E. B. Davies Analysis on graphs and noncommutative geometry M. Demuth On stochastic spectral analysis and asymptotics for Schrodinger operators P. Duclos A global approach to the location of quantum resonances v. v. Egorov On negative spectrum of elliptic operators V. EnB Non-threshold states of long-range N-body problems B. Gramsch -algebras and microlocal analysis P. B. Gilkey On the index of geometrical operators for Riemannian manifolds with boundary B. Helffer Spectral problems in statistical mechanics R. Hempe I Second order pertubations of elliptic operators with periodic principal part T. Ichinose On the Weyl quantized relativistic Hamiltonian V. V.

Die Theorie des NEWToNschen Potentials von Massenverteilungen im Raum ist eines der altesten Beispiele einer Verbindung von physikalischer Anschauung und mathematischer Interpretation. Bedeutende Mathematiker vieler Generationen, wie C. F. GAUSS, H. POINCARE, D. lIILEERT, N. WIENER haben daran mitgearbeitet. Die Entwicklung der modernen Potentialtheorie ist auch wesentlich durch die Arbeiten von G. C. EVANS, M. RIEsz, O. FBOSTMAN, M. V. KELDYs, M. BRELoT, H. CARTAN, J. DENY, G. CHOQUET, J. L. DooE, H. BAUER, C. CONSTANTINESCU, V. G. MAz 'JA, B. FUGLEDE und anderen bestimmt worden. Historische Darstellungen wurden z. B. in [K6], [A30], [B40] gegeben. Obwohl einige Teile der Potentialtheorie heute als im wesentlichen abgeschlossen gelten, hat sich die Entwicklung in den letzten Jahren wieder erheblich verstarkt, seit sich viele ihrer leistungsfahigen Begriffe und Methoden durch den zunehmenden Einsatz funktionalanalytischer Methoden auf weite Klassen von Problemen aus der Theorie der partiellen Differentialgleichungen anwenden lassen. Daneben sind in der Analysis auch davon unabhangige Bestrebungen von potentialtheoretischem Charakter zu beobachten.

This volume presents a systematic and mathematically rigorous exposition of methods for studying linear partial differential equations. It focuses on quantization of the corresponding objects (states, observables and canonical transformations) in the phase space. The quantization of all three types of classical objects is carried out in a unified way with the use of a special integral transform. This book covers recent as well as established results, treated within the framework of a universal approach. It also includes applications and provides a useful reference text for graduate and research-level readers.