3 citations · 4 across the 12 of their papers we have counts for
13 papers
A Variant of the Fractional Gamma-regularized Zeta Kernel
Hunduma Legesse Geleta
In this paper, we introduce and study a special function, referred to as a variant of the fractional gamma-regularized zeta kernel, in which the lower incomplete gamma function app…
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…
Automorphic Integrals with Rational Period Functions and Arithmetical Identities
Tewlede G/Egziabher, Hunduma Legesse Geleta, Abdul Hassen
In 1961, Chandrasekharan and Narasimhan showed that for a large class of Dirichlet series the functional equation and two types of arithmetical identities are equivalent. In 1992,…
A new proof of the corona problem
Hunduma Legesse Geleta
The corona problem was motivated by the question of the density of the open unit disc in the maximal ideal space of the algebra of bounded holomorphic functions on the unit disc. T…
Curves formed by Vanishing Discriminant and Roots of Complex-valued Harmonic Polynomials (Computer-Aided Case Study)
Oluma Ararso Alemu, Hunduma Legesse Geleta
In this paper, we determine and specify the type of curves formed by the vanishing discriminant of some specified family of complex-valued harmonic polynomials with two parameters.…
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…
More Zero-Free Regions for Fractional Hypergeometric Zeta Functions
Demessie Ergabus Birmechu, Hunduma Legesse Geleta
Some zero-free regions were known on the right half of the complex plane in the form of vertical strips for fractional hypergeometric zeta functions. In this paper, we describe and…
Automorphic Integrals with Log-polynomial Period Functions and Arithmetical Identities
Tewlede G/Egziabher, Hunduma Legesse Geleta, Abdul Hassen
Building on the works of S. Bochner on equivalence of modular relation with functional equation associated to the Dirichlet series, K. Chandrasekharan and R. Narasimhan obtained ne…
Zeros of a Two-parameter Family of Harmonic Quadrinomials
Oluma Ararso Alemu, Hunduma Legesse Geleta
In this paper, we determine the numb er of zeros and the zero inclusion regions of a two-parameter family of harmonic quadrinomials. We also determine a curve that separates sense-…