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<i>M</i> ‐functions for closed extensions of adjoint pairs of operators with applications to elliptic boundary problems
91
Citations
20
References
2009
Year
Spectral TheoryElliptic Boundary ProblemsElliptic EquationNonlinear Functional AnalysisEngineeringResolvent KernelSpectral BehaviourElliptic OperatorsClosed ExtensionsFunctional AnalysisSpectral PointsAdjoint PairsElliptic Function
Abstract In this paper, we combine results on extensions of operators with recent results on the relation between the M ‐function and the spectrum, to examine the spectral behaviour of boundary value problems. M ‐functions are defined for general closed extensions, and associated with realisations of elliptic operators. In particular, we consider both ODE and PDE examples where it is possible for the operator to possess spectral points that cannot be detected by the M ‐function (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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