Compact Hankel operators on multiply connected domains

On subnormal operators whose spectrum are multiply connected domains

Let Ω be a connected bounded domain with a finite amount of “holes” and “nice boundary”. We study subnormal operators with spectrum equal to Ω, while the spectrum of their normal extensions are supported on the boundary, ∂Ω.

Localization Principle for Compact Hankel Operators

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Toeplitz Operators in Multiply Connected Regions

Stochastic Loewner evolution in multiply connected domains

We construct radial stochastic Loewner evolution in multiply connected domains, choosing the unit disk with concentric circular slits as a family of standard domains. The natural driving function or input is a diffusion on the associated moduli space. The diffusion stops when it reaches the boundary of the moduli space. We show that for this driving function the family of random growing compact...

Schwarz-christoffel Mapping of Multiply Connected Domains

A Schwarz-Christoffel mapping formula is established for polygonal domains of finite connectivity m ≥ 2 thereby extending the results of Christoffel (1867) and Schwarz (1869) for m = 1 and Komatu (1945), m = 2. A formula for f, the conformal map of the exterior of m bounded disks to the exterior of m bounded, disjoint polygons, is derived. The derivation characterizes the global preSchwarzian f...