Related papers: Quaternionic Nevanlinna Functions

Based on the so-called re-scaling method, we will give a detailed description of the solutions to the Hamiltonian system (\ref{Hsystem}) below, which was discovered only recently by Kecker, and is strongly related to Painleve's fourth…

Properties of four quintic theta functions are developed in parallel with those of the classical Jacobi null theta functions. The quintic theta functions are shown to satisfy analogues of Jacobi's quartic theta function identity and…

This paper deals with the quantitative Schmidt's subspace theorem and the general from of the second main theorem, which are two correspondence objects in Diophantine approximation theory and Nevanlinna theory. In this paper, we give a new…

In this paper, we introduce certain $n$-th order nonlinear Loewy factorizable algebraic ordinary differential equations for the first time and study the growth of their meromorphic solutions in terms of the Nevanlinna characteristic…

The paper presents new and known results on estimates of important linear and nonlinear approximation characteristics of generalized Wiener classes of functions of several variables in different metrics.

Let $\Lambda$ be the von Mangoldt function and $r_{Q}\left(n\right)=\sum_{m_{1}+m_{2}^{2}+m_{3}^{2}=n}\Lambda\left(m_{1}\right)$ be the counting function for the numbers that can be written as sum of a prime and two squares (that we will…

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…

Slice Fueter-regular functions, originally called slice Dirac-regular functions, are generalized holomorphic functions defined over the octonion algebra $\mathbb{O}$, recently introduced by M. Jin, G. Ren and I. Sabadini. A function…

We consider the ratio of two Gauss hypergeometric functions with real parameters shifted by arbitrary integers. We find a formula for the jump of this ratio over the branch cut in terms of a real hypergeometric polynomial, the beta density…

We study the Gnedin-Kingman graph, which corresponds to Pieri's rule for the monomial basis $\{M_{\lambda}\}$ in the algebra $\mathrm{QSym}$ of quasisymmetric functions. The paper contains a detailed announcement of results concerning the…

The theory of slice regular functions of a quaternionic variable on the unit ball of the quaternions was introduced by Gentili and Struppa in 2006 and nowadays it is a well established function theory, especially in view of its applications…

We introduce an extension of the diagrammatic rules in random matrix theory and apply it to nonhermitean random matrix models using the 1/N approximation. A number of one- and two-point functions are evaluated on their holomorphic and…

In this paper, we firstly give the definition of meromorphic function element and algebroid mapping. We also construct the algebroid function family in which the arithmetic, differential operations is closed. On basis of these works, we…

Nevanlinna functions are meromorphic functions with a finite number of asymptotic values and no critical values. In [KK2] it was proved that if the orbits of all the asymptotic values accumulate on a compact set on which the function acts…

Classically, theorems of Fatou and Julia describe the boundary regularity of functions in one complex variable. The former says that a complex analytic function on the disk has non-tangential boundary values almost everywhere, and the…

The main result shows a small perturbation of a univalent function is again a univalent function, hence a univalent function has a neighborhood consisting entirely of univalent functions. For the particular choice of a linear function in…

Necessary and sufficient conditions for reducidibility of a self-adjoint linear relation in a Krein space are given. Then a generalized Nevanlinna function $Q$, represented by a self-adjoint linear relation $A$, is decomposed by means of…

We propose a definition of sampling set for the Nevanlinna class in the disk, i.e. a subset of the disk such that the analogue of the norm of a function in the Nevanlinna class can be recovered only from its values on the subset. We show it…

The use of charge balance functions in heavy-ion collision studies was initially proposed as a probe of delayed hadronization and two-stage quark production in these collisions. It later emerged that general balance functions can also serve…

This paper addresses particular eigenvalue problems within the context of two quaternionic function theories. More precisely, we study two concrete classes of quaternionic eigenvalue problems, the first one for the slice derivative operator…