Spectral Properties of the Cauchy Operator and the Operator of Logarithmic Potential Type on L2 Space With Radial Weight

Milutin Dostanić

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Spectral properties of a certain class of Carleman operators

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Domain perturbations, capacity and shift of eigenvalues

André Noll (1999)

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After introducing the notion of capacity in a general Hilbert space setting we look at the spectral bound of an arbitrary self-adjoint and semi-bounded operator $H$ . If $H$ is subjected to a domain perturbation the spectrum is shifted to the right. We show that the magnitude of this shift can be estimated in terms of the capacity. We improve the upper bound on the shift which was given in (, 24:759–775, 1999) and obtain a lower bound which leads to a generalization of Thirring’s inequality...