Blaschke-type conditions in unbounded domains, generalized convexity and   applications in perturbation theory
  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. 
S. Favorov and L. Golinskii
math.CV math.SP