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

2012/04/19 by Favorov, S., Golinskii, L.
#31A05 (Primary) 47A55 #47B10 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1204.4283

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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