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We introduce a new metric characteristic of dimensional type for non-rectifiable curves in the complex plane and use it to solve the so-called jump problem, i.e. the boundary value problem for determination of a holo-morphic function with a given jump on a given curve.
We examine Van Vleck’s Theorem on continued fractions using Möbius transformations and hyperbolic geometry. Möbius transformations can be defined in several dimensions, so we are able to obtain new results related to Van Vleck’s Theorem that are valid in many dimensions.
In this paper we introduce and investigate functions of ω-bounded type in the half-plane. We also investigate some properties of the Banach spaces Aω,γp which are natural subsets of functions of ω-bounded type, as Hardy classes are in Nevanlinna’s class N. The classes of δ-subharmonic functions...
We study the behaviour of repeated compositions of different analytic functions taken from a family
that only contain self-maps of a hyperbolic subdomain of ℂ. We generalize a result of A. F. Beardon to the case where the closure of the semi-group
, consisting of all...
A sufficient condition for a cluster point of a C
1-functio on ℝ2 to be an asymptotic value is given, based on a partitioning into regions of constant valence. We also obtain a sufficient condition for the cluster set of a planar harmonic function to have non-empty interior. An example is given...
New series developments for monogenic functions are presented. The terms of these series have factors that are expressible as power functions vanishing on special higher codimension submanifolds of Euclidean space. These series are closely related with the Cauchy-Kowalewski extension problem as...
This paper is a continuation of the author’s previous research into functions of the form...
A numerical algorithm is presented for the computation of the Schottky-Klein prime function on the Schottky double of multiply connected circular domains in the plane. While there exist classical formulae for the Schottky-Klein prime function in the form of infinite products over a Schottky...
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