Boundary Value Problems and Singular Pseudo-Differential Operators

ISBN-13: 9780471975571 / Angielski / Twarda / 1998 / 350 str.

Bert-Wolfgang Schulze;Schultz

Opis

This book 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. It features 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 asymptotics; the presentation of the algebra of boundary value problems with the transmission property, obtained as a modification of the general wedge theory; and 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.

Spis treści

Pseudo–Differential Operators.

Mellin Pseudo–Differential Operators on Manifolds with Conical Singularities.

Pseudo–Differential Calculus on Manifolds with Edges.

Boundary Value Problems.

Bibliography.

Index.

O autorze

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.

Blurb

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