Related papers: Order of growth of distributional irregular entire…

We study the rate of growth of entire functions that are frequently hypercyclic with respect to some upper weighted densities for the differentiation operator. The statements obtained show the link between the minimal growth of frequently…

We investigate the permissible growth rates of functions that are distributionally chaotic with respect to differentiation operators. We improve on the known growth estimates for $D$-distributionally chaotic entire functions, where growth…

For the Dunkl operator $\Lambda_\alpha$ $(\alpha > -1/2)$ on the space of entire functions on the complex space C, the critical rate of growth for the integral means $M_p(f,r)$ of their hypercyclic functions $f$ is obtained. The rate of…

We solve a problem posed by A. Bonilla and K.-G. Grosse-Erdmann by constructing an entire function $f$ that is frequently hypercyclic with respect to the differentiation operator, and satisfies $M_f(r)\leq\displaystyle ce^r r^{-1/4}$, where…

In this note we study the random entire functions defined as power series $f(z) = \sum_{n=0}^\infty \frac{X_n}{n!} z^n$ with independent and identically distributed coefficients $(X_n)$ and show that, under very weak assumptions, they are…

We investigate the conjugate indicator diagram or, equivalently, the indicator function of (frequently) hypercyclic functions of exponential type for differential operators. This gives insights into growth conditions of these functions on…

We are interested in the optimal growth in terms of $L^p$-averages of hypercyclic and $\mathcal{U}$-frequently hypercyclic functions for some weighted Taylor shift operators acting on the space of analytic function on the unit disc. We…

We solve a problem posed by Blasco, Bonilla and Grosse-Erdmann in 2010 by constructing a harmonic function on $\mathbb{R}^N$, that is frequently hypercyclic with respect to the partial differentiation operator $\partial/\partial x_k$ and…

This paper is a follow-up contribution to our work [10] where we studied some spectral properties of the differential operator $D$ acting between generalized Fock spaces $\mathcal{F}_{(m,p)}$ and $\mathcal{F}_{(m,q)}$ when both exponents…

Let $A$ be a homogeneous elliptic differential operator of order $m$ on $% \Bbb{R}^{N}$ with constant complex coefficients. A partial version of the main result is as follows: Suppose that $u\in L_{loc}^{1}$ and that $Au\in L^{p}$ for some…

For higher order integral functionals with $p(x)$ growth with respect to the highest order derivative $D^m u$, we prove that $D^m u$ is H\"older continuous on an open subset $\Omega_0 \subset \Omega$ of full Lebesgue- measure, provided that…

The paper aims at finding widely and smoothly defined nonparametric location and scatter functionals. As a convenient vehicle, maximum likelihood estimation of the location vector m and scatter matrix S of an elliptically symmetric t…

This article tackles the problem of existence and classification of maximal growth distributions on smooth manifolds. We show that maximal growth distributions of rank$>2$ abide by a full $h$-principle in all dimensions. We make use of M.…

We characterize lower growth estimates for subsolutions in halfspaces of fully nonlinear partial differential equations on the form $$ F(x,u,Du,D^2u) = 0 $$ in terms of solutions to ordinary differential equations built solely upon a growth…

Let $0<p<\infty$ and $0\leq q<\infty$. For each $f$ in the weighted Hardy space $H_{p, q}$,\ we show that $d\|f_r\|_{p,q}^p/dr$ grows at most like $o(1/1- r)$ as $r\rightarrow 1$.

The aim of this paper is to characterize continuous endomorphisms in the space of entire functions of exponential type of order $p>0$. Let $A_p$ denote the space of entire functions of $n$ complex variables $z\in{\mathbb C}^n$ of order $p$…

We show that a linear differential equation whose coefficients are entire functions of completely regular growth may have an entire solution of finite order which is not of completely regular growth. This answers a question of Gol'dberg and…

In 2013, Sun conjectured that the partition function $p(n)$ is never a perfect power for $n \geq 2$. Building on this, Merca, Ono, and Tsai recently observed that for any fixed integers $d \geq 0$ and $k \geq 2$, there appear to be only…

Let $T$ be a finite tree graph, $T^N$ be the Cartesian power graph of $T$, and $d^N$ be the graph distance metric on $T^N$. Also let \[ \mathbb S_r^N(x) := \{v \in T^N: d^N(x,v) = r\} \] be the sphere of radius $r$ centered at $x$ and $M$…

Given an orientation-preserving diffeomorphism of the interval [0;1], consider the uniform norm of the differential of its n-th iteration. We get a function of n called the growth sequence. Its asymptotic behaviour is an interesting…