Convolution Operators and Zeros of Entire Functions

Convolution Operators and Entire Functions with Simple Zeros

Let G(z) be an entire function of order less than 2 that is real for real z with only real zeros. Then we classify certain distribution functions F such that the convolution (G ∗ dF )(z) = ∫∞ −∞ G(z − is) dF (s) of G with the measure dF has only real zeros all of which are simple. This generalizes a method used by Pólya to study the Riemann zeta function.

Subordination and Super Ordination Results Involving Certain Convolution Operators

Subordination and Superordination Properties for Convolution Operator

In present paper a certain convolution operator of analytic functions is defined. Moreover, subordination and superordination- preserving properties for a class of analytic operators defined on the space of normalized analytic functions in the open unit disk is obtained. We also apply this to obtain sandwich results and generalizations of some known results.

Entire functions sharing a small entire function‎ ‎with their difference operators

In this paper, we mainly investigate the uniqueness of the entire function sharing a small entire function with its high difference operators. We obtain one results, which can give a negative answer to an uniqueness question relate to the Bruck conjecture dealt by Liu and Yang. Meanwhile, we also establish a difference analogue of the Bruck conjecture for entire functions of order less than 2, ...

Ahiezer-kac Type Fredholm Determinant Asymptotics for Convolution Operators with Rational Symbols

Fredholm determinant asymptotics of convolution operators on large finite intervals with rational symbols having real zeros are studied. The explicit asymptotic formulae obtained can be considered as a direct extension of the Ahiezer-Kac formula to symbols with real zeros.