On Certain Entire Functions

Certain Hilbert Spaces of Entire Functions

1. Introduction. The research reported on in the present note was motivated by the following Proposition (F), due to Ernest Fischer ([5], see also [4] for an earlier version; actually Fischer proved a more general result, but the special case suffices as a point of departure for our discussion) : (F) Let P denote a homogeneous polynomial in si, • • • , z k with complex coefficients. Then every ...

On the Arithmetical Properties of Certain Entire Characteristic Functions

A Theorem on Entire Functions

Let G(k) = ∫ 1 0 g(x)e kxdx, g ∈ L1(0, 1). The main result of this paper is the following theorem. THEOREM 1. There exists g 6≡ 0, g ∈ C∞ 0 (0, 1), such that G(kj) = 0, kj < kj+1, limj→∞ kj =∞, limk→∞ |G(k)| does not exist, lim supk→+∞ |G(k)| = ∞. This g oscillates infinitely often in any interval [1− δ, 1], however small δ > 0 is. MSC: 30D15, 42A38, 42A63

On Certain Multivalent Functions

Let ᏿ * (p,α) be the class of functions f (z) which are analytic and p-valently starlike of order α in the open unit disk E. The object of the present paper is to derive an interesting condition for f (z) to be in the class ᏿ * (p,α). This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution , and reproduction in any ...

On Sandwich theorems for certain classes of analytic functions

The purpose of this present paper is to derive some subordination and superordination results for certain analytic functions in the open unit disk. Relevant connections of the results, which are presented in the paper, with various known results are also considered.