Related papers: A uniqueness problem for entire functions related …
Let K be a non archimedean algebraically closed field of characteristic pi complete for its ultrametric absolute value. In a recent paper by Escassut and Yang, polynomial decompositions P(f)=Q(g) for meromorphic functions f, g on K (resp.…
We provide an alternative definition for the familiar concept of regular singularity for meromorphic connections. Our new formulation does not use derived categories, and it also avoids the necessity of finding a special good filtration as…
In this paper, the Neyman-Pearson lemma for general sublinear expectations is studied. We weaken the assumptions for sublinear expectations in [1] and give a completely new method to study this problem. Applying Mazur-Orlicz Theorem and the…
We investigate the famous conjecture by Erd\H os-Simonovits and Sidorenko using information theory. Our method gives a unified treatment for all known cases of the conjecture and it implies various new results as well. Our topological type…
In this paper we prove a number of results concerning uniqueness of a meromorphic function as well as its derivative sharing one or two sets. In particular, we deal with the specific question raised in [18], [19], [20] and ultimately…
In 2016 and 2017, Haihui Fan, Don Hadwin and Wenjing Liu proved a commutative and noncommutative version of Beurling's theorems for a continuous unitarily invariant norm $\alpha $ on $L^{\infty}(\mathbb{T},\mu)$ and tracial finite von…
In this paper, we study the growth, in terms of the Nevanlinna characteristic function, of meromorphic solutions of three types of second order nonlinear algebraic ordinary differential equations. We give all their meromorphic solutions…
We obtain some Liouville type theorems for positive harmonic functions on compact Riemannian manifolds with nonnegative Ricci curvature and strictly convex boundary and partially verifies Wang's conjecture (J. Geom. Anal. 31 (2021)). For…
Given any infinite tree in the plane satisfying certain topological conditions, we construct an entire function $f$ with only two critical values $\pm 1$ and no asymptotic values such that $f^{-1}([-1,1])$ is ambiently homeomorphic to the…
For two meromorphic functions $ f $ and $ g $, the equation $ f^m+g^m=1 $ can be regarded as Fermat-type equations. Using Nevanlinna theory for meromorphic functions in several complex variables, the main purpose of this paper is to…
In this article we consider the class $\mathcal{A}(p)$ which consists of functions that are meromorphic in the unit disc $\ID$ having a simple pole at $z=p\in (0,1)$ with the normalization $f(0)=0=f'(0)-1 $. First we prove some sufficient…
We consider a class of weighted harmonic functions in the open upper half-plane known as $\alpha$-harmonic functions. Of particular interest is the uniqueness problem for such functions subject to a vanishing Dirichlet boundary value on the…
This thesis extends the Hoffman-Rudolph tvwB criterion defined for uniformly p-to-1 endomorphisms to show that it still gives a sufficient condition for a given $\bf p$-endomorphism to be one-sided Bernoulli. We also prove that given any…
Taking as model the attractor of an iterated function system consisting of phi-contractions on a complete and bounded metric space, we introduce the set-theoretic concept of family of functions having attractor. We prove that, given such a…
There have been, over the last 8 years, a number of far reaching extensions of the famous original F. and M. Riesz's uniqueness theorem that states that if a bounded analytic function in the unit disc of the complex plane $\Bbb C$ has the…
We prove a non-vanishing result for families of $\GL_n\times\GL_n$ Rankin-Selberg $L$-functions in the critical strip, as one factor runs over twists by Hecke characters. As an application, we simplify the proof, due to Luo, Rudnick, and…
This note finds a new characterization of complete Nevanlinna-Pick kernels on the Euclidean unit ball. The classical theory of Sz.-Nagy and Foias about the characteristic function is extended in this note to a commuting tuple $\bfT$ of…
We study the eigenvalue problem for a superlinear convolution operator in the special case of bilinear constitutive laws and establish the existence and uniqueness of a one-parameter family of nonlinear eigenfunctions under a topological…
We have established various criteria for the topological transitivity of families of continuous (holomorphic) functions. Furthermore, by leveraging the properties of expanding families of meromorphic functions, we offer an alternative proof…
We prove Runge-type theorems and universality results for locally univalent holomorphic and meromorphic functions. Refining a result of M. Heins, we also show that there is a universal bounded locally univalent function on the unit disk.…