Interpolation and Uniqueness Results for Entire Functions

Further Results on Uniqueness of Entire Functions Sharing One Value

In this paper, we study the uniqueness problems of entire functions sharing one value with weight l (l = 0,1,2). The results in this paper improve the related results given by X.Y. Zhang and W.C. Lin, M.L. Fang, C.C. Yang and X.H. Hua, etc.

Interpolation and Approximation by Entire Functions

In this note we study the connection between best approximation and interpolation by entire functions on the real line. A general representation for entire interpolants is outlined. As an illustration, best upper and lower approximations from the class of functions of fixed exponential type to the Gaussian are constructed. §1. Approximation Background The Fourier transform of φ ∈ L(R) is define...

Uniqueness theorems of entire and meromorphic functions sharing small function

In this paper, we deal with some uniqueness theorems of two transcendental meromorphic functions with their non-linear differential polynomials sharing a small function. These results in this paper improve those given by of Fang and Hong [M.L.Fang and W.Hong,A unicity theorem for entire functions concerning differential polynomials,Indian J.Pure Appl.Math.32.(2001),No.9,1343-1348.], I.Lahiri an...

Interpolation of entire functions, product formula for basic sine function

q-Taylor theorems, polynomial expansions, and interpolation of entire functions

We establish q-analogues of Taylor series expansions in special polynomial bases for functions analytic in bounded domains and for entire functions whose maximum modulus Mðr; f Þ satisfies jln Mðr; f ÞjpA ln r: This solves the problem of constructing such entire functions from their values at 1⁄2aq þ q =a =2; for 0oqo1: Our technique is constructive and gives an explicit representation of the s...