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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Smooth Spectral Calculus
verfasst von : Matania Ben-Artzi
Erschienen in: Partial Differential Equations and Spectral Theory
Verlag: Springer Basel
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A smooth spectral theory is presented in an abstract Hilbert space framework. The main assumption (of smoothness) is the Hölder continuity of the derivative of the spectral measure (density of states). A Limiting Absorption Principle (LAP) is derived on the basis of continuity properties of Cauchytype integrals. This abstract theory is then extended to include short-range perturbations and sums of tensor products. Applications to partial differential operators are presented. In the context of partial differential operators the spectral derivative is closely related to trace operators on compact (for elliptic operators) or non-compact manifolds.