Complex Variables and Elliptic Equations 

About: Complex Variables and Elliptic Equations is an academic journal published by Taylor & Francis. The journal publishes majorly in the area(s): Bounded function & Holomorphic function. It has an ISSN identifier of 1747-6933. Over the lifetime, 3090 publications have been published receiving 22521 citations. The journal is also known as: Complex variables & Complex variables and elliptic equations.

Weighted value sharing and uniqueness of meromorphic functions

Abstract: With the and of the notion of weighted sharing we prove some uniqueness theorems of meromorphic functions which improve some earlier results

An integral operator on $H\sp p$

Abstract: Let g be an analytic function on the unit disk D . We study the operator on the Hardy spaces Hp . We show that Tg is bounded on Hp , 1 ≤ p < ∞ it and only if g ∊ BMOA and compact if and only if g ∊ VOMA. Further on the Hilbert space H2 Tg is in the Schattcn ρ-class it and only if g is in the Besov space Bp , 1 < p < ∞. A relation of Tg with integration operators is also discussed.

A hypercomplex derivative of monogenic functsions in and its Applications

Abstract: We generalize the definition of a certain derivative of regular functions of variables from the four-dimensional real associative algebra of quaternions to monogenic functions of hypercomplex variables in Rn+1. Using this concept of derivation we look for primitives of monogenic functions in the set of monogenic functions. The results will be applied for proving a final result about the invertibility of a hypercomplex II-operator.

Extremal length geometry of teichmüller space

Abstract: Assume τ is a point in the Teichmuller space of a Riemann surface which is compact or obtainable from a compact surface by deleting a finite number of punctures. Let be extermal lengths of two transversely realizable measured folitions on the Riemann surface R r corresponding to the point τ. There is a unique Teichmuller line along which the function is minimum. Teichmuller space embeds into projective classes of vectors of square roots of extremal lengths of simple curves on the base surface. The closure of the image of Teichmuller space under this embedding is compact. Moreover, there is a relationship between the boundary of this embedding and the boundary of the extremal length embedding properly contains the Thruston boundary.

Extremal domains associated with an analytic function I

Abstract: In this paper we investigate the following two extremal problems: A) Let F be a continuum in the extended complex plane that does not divide and let f(z) be a function analytic on F By D we denote domains in such that f(z) has a single-valued analytic continuation in D. Does there exist a domain D 0 with minimal condenser capacity B) Let f(z) be a function analytic in a neighborhood of infinity. By D we denote domains in , such that f{z) has a single-valued analytic continuation in D. Does there exist a domain D 0 with minimal logarithmic capacity It is proved that there exist extremal domains D 0 in both problems. In a second part of the paper it will be shown that these domains are uniquely determined up to a boundary set of capacity zero.