Related papers: Entire functions with separated zeros and $1$-poin…
Recently Bishop constructed the first example of a bounded-type transcendental entire function with a wandering domain using a new technique called quasiconfomal folding. It is easy to check that his method produces an entire function of…
It is shown that harmonic functions on some subsets, subharmonic and coinciding everywhere outside of these sets, actually coincide everywhere.
This article provide new approach to solve P vs NP problem by using cardinality of bases function. About NP-Complete problems, we can divide to infinite disjunction of P-Complete problems. These P-Complete problems are independent of each…
A class theorem is presented and proved: the complex Fourier transforms of a certain class of exponential functions have all their zeros on the real line. A class of basis functions is first considered, and the class is then extended via…
We consider the entire characteristic functions of order 2 and we prove some decomposition theorems in a multidimensional case. We show that the lack of zeros of the density function is a necessary but not a sufficient (as in the…
We show that there exists an entire function which has neither fixed points nor invariant Baker domains. The question whether such a function exists was raised by Buff.
We study how the orbits of the singularities of the inverse of a meromorphic function prescribe the dynamics on its Julia set, at least up to a set of (Lebesgue) measure zero. We concentrate on a family of entire transcendental functions…
We introduce the concept of escaping set for semigroups of transcendental entire functions using Fatou-Julia theory. Several results of the escaping set associated with the iteration of one transcendental entire function have been extended…
We extend to several variables an earlier result of ours, according to which an entire function of one variable of sufficiently small exponential type, having all derivatives of even order taking integer values at two points, is a…
In this paper, we study all possible orders which are less than 1 of transcendental entire solutions of linear difference equations \begin{equation} P_m(z)\Delta^mf(z)+\cdots+P_1(z)\Delta f(z)+P_0(z)f(z)=0,\tag{+} \end{equation} where…
In this work we verify the sufficiency of a Jensen's necessary and sufficient condition for a class of genus 0 or 1 entire functions to have only real zeros. They are Fourier transforms of even, positive, indefinitely differentiable, and…
The main result of this paper shows a totally new necessary and sufficient condition to determine both real and complex zeros of derivative of all entire and meromorphic functions of one complex variable in the extended complex plane. By…
Let $\Omega$ be a bounded domain in $\mathbb{C}$ such that $\partial \Omega$ does not contain isolated points. Let $R(\Omega)$ be the space of uniform limits on $\overline{\Omega}$ of rational functions with poles off $\overline{\Omega}$,…
We introduce a new approximation technique into the context of complex dynamics that allows us to construct examples of transcendental entire functions with unbounded wandering domains. We provide examples of entire functions with an orbit…
We consider distributions on $\mathbb{R}$ that can be written as the sum of a non-zero discrete distribution and an absolutely continuous distribution. We show that such a distribution is quasi-infinitely divisible if and only if its…
We study certain integer valued length functions on triangulated categories and establish a correspondence between such functions and cohomological functors taking values in the category of finite length modules over some ring. The…
We show that if a complex entire function $f$ and its derivative $f'$ share their simple zeroes and their simple $a$-points for some nonzero constant $a$, then $f\equiv f'$. We also discuss how far these conditions can be relaxed or…
We consider transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. Based on their classification in [B3] we investigate their dependence on…
In this paper, we study the value distribution of zeros of certain nonlinear difference polynomials of entire functions of finite order.
This paper deals with a new kind of generalized functions, called "ultrafunctions" which have been introduced recently and developed in some previous works. Their peculiarity is that they are based on a Non-Archimedean field namely on a…