The zeros of a certain entire function

Sums of an Entire Function in Certain Weighted L-spaces

A Problem Concerning the Zeros of a Certain Kind of Holomorphic Function in the Unit Disk

To Hehzut Hasse on his 6~. birthday Let f(a) be a holomorphic. function in the open unit disk D in the complex plane. (b) given any 8 > 0, there exists an n, = no(&) suc,h that, for every IL > rtO, J, lies in the region 1-E < 1 z 1 < 1. Set p!c, = p$ I f(z) I If lim pu, = 00, then we call f, for brevity, an annular function.-CO As is evident from this definition, an annular fun&ion f is not ide...

Asymptotics of Zeros for Some Entire Functions

We study the asymptotics of zeros for entire functions of the form sin z+ ∫ 1 −1 f(t)e dt with f belonging to a space X →֒ L1(−1, 1) possessing some minimal regularity properties.

Convolution Operators and Zeros of Entire Functions

Let G(z) be a real entire function of order less than 2 with only real zeros. Then we classify certain distributions functions F such that the convolution (G ∗ dF )(z) = ∫∞ −∞G(z − is) dF (s) has only real zeros.

The Zeros of Certain Lommel Functions

Lommel’s function sμ,ν(z) is a particular solution of the differential equation z2y′′ + zy′ + (z2 − ν2)y = zμ+1. Here we present estimates and monotonicity properties of the positive zeros of sμ−1/2,1/2(z) when μ ∈ (0, 1). The positivity of a closely related integral is also considered.