On location in a half-plane of zeros of perturbed first order entire functions

Mathematica Moravica

Gil Michael¹ 

[1] Ben Gurion University of the Negev, Department of Mathematics, Beer-Sheva, Israel;

关键词: Entire functions;    zeros;    perturbations;   

DOI  :  

来源: DOAJ

【 摘 要 】

We consider the entire functions h(z) = X∞ k=0 akz k k! and h~(z) = X∞ k=0 a~kz k k! (a0 = ~a0 = 1; z, ak, a~k ∈ C, k = 1, 2, . . .), provided X∞ k=0 |ak| 2 < ∞, X∞ k=0 |a~k| 2 < ∞ and all the zeros of h(z) are in a half-plane. We investigate the following problem: how small should be the quantity q := (P∞ k=1 |ak - a~k| 2 ) 1/2 in order to all the zeros of h~(z) lie in the same half-plane?

【 授权许可】

Unknown