Displaying similar documents to “Spectral Properties of the Cauchy Operator and the Operator of Logarithmic Potential Type on L2 Space With Radial Weight”

Spectral properties of a certain class of Carleman operators

S. M. Bahri (2007)

Archivum Mathematicum

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The object of the present work is to construct all the generalized spectral functions of a certain class of Carleman operators in the Hilbert space L 2 X , μ and establish the corresponding expansion theorems, when the deficiency indices are (1,1). This is done by constructing the generalized resolvents of A and then using the Stieltjes inversion formula.

Domain perturbations, capacity and shift of eigenvalues

André Noll (1999)

Journées équations aux dérivées partielles

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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...