An Entire Holomorphic Function Associated to an Entire Harmonic Function

An Entire Function with Simply and Multiply Connected Wandering Domains

We modify a construction of Kisaka and Shishikura to show that there exists an entire function f which has both a simply connected and a multiply connected wandering domain. Moreover, these domains are contained in the set A(f) consisting of the points where the iterates of f tend to infinity fast. The results answer questions by Rippon and Stallard.

On Relations among Some Constants of an Entire Function

If Piz) is an entire function of order p, it is known that (1) M, m are its type and co-type, in case/ happens to be the rank (or position) function of the maximum term of the Maclaurin series of P (see Chapter II of [l] and Chapter II of [2]) and that (2) M and m are the logarithmic type and co-type of P, if fix) is the number of zeroes z of Piz) such that \z\ ^x (see Jensen's Theorem, Chapter...

Sums of an Entire Function in Certain Weighted L-spaces

A property of the derivative of an entire function

We prove that the derivative of a non-linear entire function is unbounded on the preimage of an unbounded set. MSC 2010: 30D30.

The Set on Which an Entire Function Is Small

Let f (z) be an entire function and M(r) the maximum of I f (z) on z = r . We give some results on the density of the set of points at which f (z) I is small in comparison with M(r) ; although simple, these results seem not to have been noticed before . If E is a measurable set in the z-plane, we denote by DR (E) the ratio m(z c E, I z < R)/1rRZ and by D(E) and D(E) the upper and lower densitie...