Items related to Spectral Theory, Microlocal Analysis, Singular Manifolds
Synopsis
The spectral theory of differential operators is a challenging subject with deep connections to many branches of mathematics and mathematical physics. It is a central issue in this volume of Advances in Partial Differential Equations
The first contribution addresses domain perturbations for generalized Schrödinger operators and the influence of the capacity on spectral data. There follows an article discussing the minimal smoothness assumptions on the domain under which the asymptotics of the counting function for the eigenvalues of elliptic boundary value problems can be determined. Systems of h-pseudo-differential operators on the half-line are studied in the next paper. The results concern existence and distribution of resonances for various semi-classical regimes.
Three further articles are devoted to the regularity and symptotics of solutions to partial differential equations on singular manifolds. A very efficient tool is the combination of suitable operator algebras and pseudo-differential calculi with sufficiently rich symbolic structures. One paper considers the case of manifolds with non-compact ends, another the case of higher cuspidal singularities. A final contribution treats degenerate hyperbolic equations.
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From the Publisher
The material found in this book is from a series originating from the work of the Max Planck Research Group for Partial Differential Equations and Complex Analysis at the University of Potsdam, Germany. It is the intention of the editor to promote expositions of a systematic character in the field of partial differential equations.
About the Author
Michael Demuth, Prof. Dr., Technical University of Clausthal; Elmar Schrohe, Dr., and Bert-Wolfgang Schulze, Prof. Dr., both University of Potsdam; Johannes Sjöstrand, Prof. Dr., Ecole Polytechnique, Palaiseau
"About this title" may belong to another edition of this title.
- PublisherWiley-VCH
- Publication date1998
- ISBN 10 3527401202
- ISBN 13 9783527401208
- BindingPaperback
- LanguageEnglish
- Edition number1
- Number of pages368
- EditorDemuth Michael, Schrohe Elmar, Schulze Bert-Wolfgang, Sjöstrand Johannes
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