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

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

2012-04-19

arxiv.org/abs/1204.4283v1

Mathematics

Complex Variables

17 pages

Scientific paper

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.

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