13 research outputs found
Meromorphic Approximants to Complex Cauchy Transforms with Polar Singularities
We study AAK-type meromorphic approximants to functions , where is a
sum of a rational function and a Cauchy transform of a complex measure
with compact regular support included in , whose argument has
bounded variation on the support. The approximation is understood in -norm
of the unit circle, . We obtain that the counting measures of poles of
the approximants converge to the Green equilibrium distribution on the support
of relative to the unit disk, that the approximants themselves
converge in capacity to , and that the poles of attract at least as many
poles of the approximants as their multiplicity and not much more.Comment: 39 pages, 4 figure
The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function. II. The Complex Plane
The Logarithm of the Modulus of a Holomorphic Function as a Minorant for a Subharmonic Function
Prime ends in the mapping theory on the Riemann surfaces
It is proved criteria for continuous and homeomorphic extension to the boundary of mappings with finite distortion between domains on the Riemann surfaces by prime ends of Caratheodory