Related papers: Rapidly growing entire functions with three singul…
A two-parameter characteristic of functions meromorphic on annuli is introduced and an extension of the Nevanlinna value distribution theory for such functions is proposed.
We consider the classical Picard's problem for non-parabolic complete K\"ahler manifolds with non-negative Ricci curvature. Based on the global Green function approach, we give a positive answer to Picard's problem under certain condition…
Every rational Nevanlinna function in n variables is a Cayley inner function in n + 1 variables with one variable fixed in the upper half-plane.
We generalize two integral representation formulae of Nevanlinna to functions of several variables. We show that for a large class of analytic functions that have non-negative imaginary part on the upper polyhalfplane there are…
Nevanlinna's five-value theorem is well-known as a famous theorem in value distribution theory, which asserts that two non-constant meromorphic functions on $\mathbb C$ are identical if they share five distinct values ignoring…
We formulate three boundary Nevanlinna-Pick interpolation problems for generalized Nevanlinna functions. For each problem, we parameterize the set of all solutions in terms of a linear fractional transformation with an extended Nevanlinna…
The solutions of an indeterminate Hamburger moment problem can be parameterised using the Nevanlinna matrix of the problem. The entries of this matrix are entire functions of minimal exponential type, and any growth less than that can…
The minimal possible rate of growth of a meromorphic function with three critical values is found.
We solve a three point Nevanlinna-Pick problem in the Euclidean ball. In particular, we determine a class of rational functions that interpolate this problem.
We solve the following three problems. 1. How much can the radial growth of an entire function $f$ be reduced by multiplying it by some nonzero entire function? We give the answer in terms of the growth of the integral means of $\ln|f|$…
The existence of entire solutions to quadratic trinomial Fermat type differential-difference equations and \(q\)-difference differential equations involving second-order derivatives is studied by using Nevanlinna theory, and the exact form…
We give a characterization for the existence of a holomorphic interpolant on the unit polydisc $\mathbb{D}^n,$ $n\geq 2,$ for prescribed three-point Pick--Nevanlinna data. One of the key steps is a characterization for the existence of an…
We derive an integral representation for Herglotz-Nevanlinna functions in two variables which provides a complete characterization of this class in terms of a real number, two non-negative numbers and a positive measure satisfying certain…
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 prove generalizations of L\"owner's results on matrix monotone functions to several variables. We give a characterization of when a function of $d$ variables is locally monotone on $d$-tuples of commuting self-adjoint $n$-by-$n$…
A tropical version of Nevanlinna theory is described in which the role of meromorphic functions is played by continuous piecewise linear functions of a real variable whose one-sided derivatives are integers at every point. These functions…
The paper develops an equidistribution theory of meromorphic mappings from a complete K\"ahler manifold with non-negative Ricci curvature into a complex projective manifold intersecting normal crossing divisors. When the domain manifolds…
Let $U\not\equiv \pm\infty$ be the difference of subharmonic functions, i.e., a $\delta$-subharmonic function, on a closed disc of radius $R$ centered at zero. In the preceding first part of our paper, we obtained general estimates for the…
We establish the existence of Nevanlinna domains with large boundaries. In particular, these domains can have boundaries of positive planar measure. The sets of accessible points can be of any Hausdorff dimension between $1$ and $2$. As a…
Nevanlinna theory studies the value distribution of meromorphic functions and provides powerful results in the form of the First and Second Main Theorems. In this paper, we introduce quaternionic analogues of the Nevanlinna functions.…