Blaschke-type conditions in unbounded domains, generalized convexity and applications in perturbation theory

Abstract

We introduce a new geometric characteristic of compact sets on the plane called $r$-convexity, which fits nicely into the concept of generalized convexity and extends essentially the conventional convexity. For a class of subharmonic functions on unbounded domains with $r$-convex compact complement, with the growth governed by the distance to the boundary, we obtain the Blaschke--type condition for their Riesz measures. The result is applied to the study of the convergence of the discrete spectrum for the Schatten--von Neumann perturbations of bounded linear operators in the Hilbert space.

21 pages

References in corpus (2)

• Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators
• On the distribution of eigenvalues of non-selfadjoint operators

Cited by in corpus (2)

• Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators
• On the distribution of the discrete spectrum of nuclearly perturbed operators in Banach spaces