Evolution Equations, Feshbach Resonances, Singular Hodge Theory. With 14 figures

Demuth, Michael / Schrohe, Elmar / Schulze, Bert-Wolfgang / Sjöstrand, Johannes (Ed.)

ISBN 10: 3527402330 / ISBN 13: 9783527402335

Verlag: Wiley-VCH, Bln., 1999

Beschreibung

gr8 Original-Pappband 1st ed. en Equations, Mathematik, Naturwissenschaften (Mathematical Topics. Vol. 16: Advances in Partial Differential Equations); 431 pp.

Bestandsnummer des Verkäufers 1072

Bibliografische Details

• Titel: Evolution Equations, Feshbach Resonances, Singular Hodge Theory. With 14 figures
• Verlag: Wiley-VCH, Bln.
• Erscheinungsjahr: 1999
• Sprache: Englisch
• ISBN-10: 3527402330
• ISBN-13: 9783527402335
• Einband: Original-Pappband
• Zustand: Sehr gut

Über diesen Titel

Inhaltsangabe

Evolution equations describe many processes in science and engineering. The first three contributions to this volume address parabolic evolutionary problems: first there is a treatment, via asymptotic solutions, of transitions with highly singular interaction at th start, say by distribution of even hyperfunction data. An article follows on solutions to time dependent singular problems in non-cylindrical domains by local operator methods. In the third paper, the theory of the asymptotic Laplace transform is developed and applied to semigroups generated by operators with large growth of the resolvement. The next contribution addresses spectral properties of systems of pseudodifferential operators when the characteristic variety has a conical intersection. For various semiclassical regimes, Bohr-Sommerfeld quantization rules and first order exponential asymptotics of the resonance widths are provided. In the following article, the limiting absorption principle is proven for certain self-adjoint operators. Applications include Hamiltonians with magnetic fields, Dirac Hamiltonians, and propagation of waves in inhomogeneous media. The final topic is the Hodge theory on manifolds with edges. The authors introduce a concept of elliptic complexes, prove a Hodge decomposition theorem, and study the asymptotics of harmonic forms.

Von der hinteren Coverseite

Evolution equations describe many processes in science and engineering, and they form a central topic in mathematics. The first three contributions to this volume address parabolic evolutionary problems: The opening paper treats asymptotic solutions to singular parabolic problems with distribution and hyperfunction data. The theory of the asymptotic Laplace transform is developed in the second paper and is applied to semigroups generated by operators with large growth of the resolvent. An article follows on solutions by local operator methods of time-dependent singular problems in non-cylindrical domains. The next contribution addresses spectral properties of systems of pseudo-differential operators when the characteristic variety has a conical intersection. Bohr-Sommerfeld quantization rules and first order exponential asymptotics of the resonance widths are established under various semiclassical regimes. In the following article, the limiting absorption principle is proven for certain self-adjoint operators. Applications include Hamiltonians with magnetic fields, Dirac Hamiltonians, and the propagation of waves in inhomogeneous media. The final topic develops Hodge theory on manifolds with edges; its authors introduce a concept of elliptic complexes, prove a Hodge decomposition theorem, and study the asymptotics of harmonic forms.