Related papers: Rapidly growing entire functions with three singul…

For an inner function $\theta$ with $\theta'\in\mathcal N$, where $\mathcal N$ is the Nevanlinna class, several problems are posed in connection with the canonical (inner-outer) factorization of $\theta'$.

Our objects of study are two-dimensional canonical systems that arise from indeterminate Hamburger moment problems and associated half-line Jacobi operators in limit circle case. The monodromy matrix of such a system coincides, up to a…

The main result of the present paper is the construction of fundamental solutions for a class of multidimensional elliptic equations with three singular coefficients, which could be expressed in terms of a confluent hypergeometric function…

Let $M$ be a compact connected smooth manifold with smooth boundary, and let $\rho$ be a positive continuous function on the boundary which is served as the Robin parameter. In this paper, we study three problems concerning the prescription…

We prove that there exists an entire function for which every complex number is an asymptotic value and whose growth is arbitrarily slow subject only to the necessary condition that the function is of infinite order.

The Sz.-Nagy Foias characteristic function for a contraction has had a rejuvenation in recent times due to a number of authors. Such a classical object relates to an object of very contemporary interest, viz., the complete Nevanlinna-Pick…

In this paper, we prove a theorem concerning the existence of three solutions for the following boundary value problem: \begin{equation*} -\mathcal{M}_{\lambda,\Lambda}^+(D^2u)-\Gamma|Du|^2=f(u)~~~\text{in}\ \Omega, u=0~~~\text{on}\…

In this paper we investigate finitely generated ideals in the Nevanlinna class. We prove analogues to some known results for the algebra of bounded analytic functions $H^{\infty}$. We also show that, in contrast to the $H^{\infty}$-case,…

We give a direct evaluation of a curious integral identity, which follows from the work of Ismail and Valent on the Nevanlinna parametrization of solutions to a certain indeterminate moment problem.

In this paper, we prove a normal criteria for family of meromorphic functions. As an application of that result, we establish a uniqueness theorem for entire function concerning a conjecture of R. Bruck. The above uniqueness theorem is an…

Let $A$ be a symmetric operator. By using the method of boundary triplets we parameterize in terms of a Nevanlinna parameter $\tau$ all exit space extensions $\wt A=\wt A^*$ of $A$ with the discrete spectrum $\s(\wt A)$ and characterize the…

We study several aspects concerning slice regular functions mapping the quaternionic open unit ball into itself. We characterize these functions in terms of their Taylor coefficients at the origin and identify them as contractive…

A crucial ingredient in the recent discovery by Ablowitz, Halburd, Herbst and Korhonen \cite{AHH}, \cite {HK-2} that a connection exists between discrete Painlev\'e equations and (finite order) Nevanlinna theory is an estimate of the…

We consider resolution of singularities for $1$-foliations on varieties of dimension at most three in positive characteristic. We prove that such singularities can be completely resolved if we allow tame regular Deligne--Mumford stacks as…

Using Nevanlinna's value distribution theory and the complex difference theory , the existence of the finite order of the entire solutions of the Fermat type of the complex differential-difference equation and the systems of complex…

We study a class of nonlinear non-autonomous nonlocal equations with subcritical and critical exponential nonlinearity. The involved potential can vanish at infinity.

This paper is dedicated to the unique continuation properties of the solutions to nonlinear variational problems. Our analysis covers the case of nonlinear autonomous functionals depending on the gradient, as well as more general double…

In this article, a characterization of the class of Herglotz-Nevanlinna functions in $n$ variables is given in terms of an integral representation. Furthermore, alternative conditions on the measure appearing in this representation are…

We construct entire curves in projective spaces that exhibit frequent hypercyclicity under translations along countably many prescribed directions while maintaining optimal slow growth rates. Furthermore, we establish a fundamental…

Let $f$ be a meromorphic function on the complex plane $\mathbb C$ with the maximum function of its modulus $M(r,f)$ on circles centered at zero of radius $r$. A number of classical, well-known and widely used results allow us to estimate…