5 papers
The Effect of Planar Harmonic Mappings on the Lebesgue Measure of Sets
Hunduma Legesse Geleta
We investigate the effect of planar univalent harmonic mappings on the Lebesgue measure of measurable sets in the complex plane. Motivated by Problem 3.25 of Koh and Kovalev (HQM20…
More on Boundary Behavior of Univalent Harmonic Mappings
Gebreslassie atsbha weldegebrial, hunduma legesse geleta
Many authors have examined various boundary behaviors of injective harmonic mappings in the open unit disk. Building on Laugesen's work, Bshouty and others explored the boundary be…
Bounded Composition Operators on Hilbert Space of Complex-Valued Harmonic Functions
Tseganesh Getachew Gebrehana, Hunduma Legesse Geleta
In this paper, we study composition operators on Hilbert space of complex-valued harmonic functions. In particular, we explore isometries, the type of self-map that generate bounde…
Boundary values and zeros of Harmonic Product of Complex-valued Harmonic Functions in a simply connected bounded Domain
Ayantu Guteta Fite, Hunduma Legesse Geleta
The product of two complex-valued harmonic function is not in general complex-valued harmonic function. In this paper we show that if a complex-valued harmonic function is the prod…
Hilbert Space of Complex-Valued Harmonic Functions in the Unit Disc
Tseganesh Getachew Gebrehana, Hunduma Legesse Geleta
We investigate an extended version of Hilbert space of analytic functions called Hilbert space of complex-valued harmonic functions. It is found that functions in Hilbert space of…