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arXiv · 1204.4283

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

S. Favorov·L. Golinskii
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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.

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S. Favorov, L. Golinskii. 2012-09-03. Blaschke-type conditions in unbounded domains, generalized convexity and applications in perturbation theory. https://arxiv.org/abs/1204.4283

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