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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…
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…
The Image of Critical Circle and Zero-free Curve for Quadrinomials
Oluma Ararso Alemu, Hunduma Legesse Geleta
The location of the zeros of a two-parameter family of complex-valued harmonic quadrinomials depends on the parameters. In this paper, we determine and demonstrate that the image o…