This note proposes an algorithm for identifying the poles and residues of a meromorphic function from its noisy values on imaginary axis. The uses Möbius transform Prony’s method in frequency domain. Numerical results are provided to demonstrate performance algorithm.

We consider any transcendental meromorphic function f of Class S whose Julia set is a Jordan curve. We show that the Julia set of f either is an extended straight line or has Hausdorff dimension strictly greater than 1. The proof uses conformal iterated function systems and extends many earlier results of this type.

In this paper, a necessary and sufficient coefficient are given for functions in a class of complex valued meromorphic harmonic univalent functions of the form f = h + ḡ using Salagean operator. Furthermore, distortion theorems, extreme points, convolution condition and convex combinations for this family of meromorphic harmonic functions are obtained. Keywords—Harmonic mappings, Meromorphic fu...

Recently, Special Function Theory (SPFT) and Operator (OPT) have acquired a lot of concern due to their considerable applications in disciplines pure applied mathematics. The Hurwitz-Lerch Zeta type functions, as part (SPFT), are significant developing providing further new studies. In complex domain, the convolution tool is salutary technique for systematic analytical characterization geometri...

Given an unbounded non-decreasing positive function φ, we studied what the relations are between growth order of any solution a complex linear differential–difference equation whose coefficients entire or meromorphic functions finite φ-order. Our findings extend some earlier well-known results.

Loo's theorem asserts that the space of all branched minimal 2spheres of degree d in 54(1) is connected. The main theorem in this paper is that the assertion is still true for S2m (1). It is shown that any branched minimal 2-sphere in S2m (1) can be deformed, preserving its degree, to a meromorphic function. 0. Introduction After the celebrated research on minimal 2-spheres in the unit sphere 5...

We consider the differential operator Λk defined by Λk(y) = Ψk(y) + ak−1Ψk−1(y) + . . .+ a1Ψ1(y) + a0 , where a0, . . . , ak−1 are analytic functions of restricted growth and Ψk(y) is a differential operator defined by Ψ1(y) = y and Ψk+1(y) = yΨk(y) + (Ψk(y)) for k ∈ N. We suppose that k ≥ 3, that F is a meromorphic function on an annulus A(r0), and that Λk(F ) has all its zeros on a set E such...

It is shown that if n ∈ N, c ∈ C, and three distinct values of a meromorphic function f : C → P of hyper-order ς(f) strictly less than 2/3 have forward invariant pre-images with respect to a translation τ : C → C, τ(z) = z + c, then f is a periodic function with period c. This result can be seen as a generalization of M. Green’s Picard-type theorem in the special case where ς(f) < 2/3, since th...