Related papers: Value distribution and linear operators
The main result of the paper determines all real meromorphic functions of finite order in the plane for which the first derivative has finitely many zeros, while the function itself and one of its higher derivatives have finitely many…
The statistical behaviour of a product of independent, identically distributed random matrices in $\text{SL}(2,{\mathbb R})$ is encoded in the generalised Lyapunov exponent $\Lambda$; this is a function whose value at the complex number $2…
A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of distribution which determines the dependency between one…
The distribution functions of the matricvariate beta type I and II distributions are studied under real normed division algebras. The unified approach for real, complex, quaternions and octonions, also considers general properties and…
In this paper, we study the uniqueness of the differential-difference of meromorphic functions. We prove the following result: Let $f$ be a nonconstant meromorphic function of $\rho_{2}(f)<1$, let $\eta$ be a non-zero complex number,…
The classical result of Nevanlinna states that two nonconstant meromorphic functions on the complex plane having the same images for five distinct values must be identically equal to each other. In this paper, we give a similar uniqueness…
The class of Dirichlet series associated with a periodic arithmetical function $f$ includes the Riemann zeta-function as well as Dirichlet $L$-functions to residue class characters. We study the value-distribution of these Dirichlet series…
In this short manuscript, we will put some light on the different outcomes when two non-constant meromorphic functions share a value with prescribed weight two.
We prove a factorization theorem for reproducing kernel Hilbert spaces whose kernel has a normalized complete Nevanlinna-Pick factor. This result relates the functions in the original space to pointwise multipliers determined by the…
In this work we prove the Stepanov differentiation theorem for multiple-valued functions. This theorem is proved in the wide generality of metric-space-multiple-valued functions without relying on a Lipschitz extension result. General…
We consider the set of power functions defined on the set of positive real number, and their linear combinations. After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative…
We show that a considerable part of the theory of (ultra)distributions and hyperfunctions can be extended to more singular generalized functions, starting from an angular localizability notion introduced previously. Such an extension is…
In this paper, we shall study the uniqueness problems on meromorphic functions sharing a polynomial. We give a complete answer to a problem posed by Fang Mingliang. Our results improve or generalize those given by Fang and Hua, Yang and…
An extension of the notion of solvable structure for involutive distributions of vector fields is introduced. The new structures are based on a generalization of the concept of symmetry of a distribution of vector fields, inspired in the…
Let f be a nonconstant meromorphic function in the plane and h be a nonconstant elliptic function. We show that if all zeros of f are multiple exept finitely many and T(r,h)=o{T(r,f)} as r tends to infinity, then f'=h has infinitely many…
The basic results for nonlinear operators are given. These results include nonlinear versions of classical uniform boundedness theorem and Hahn-Banach theorem. Furthermore, the mappings from a metrizable space into another normed space can…
In this paper, we investigate meromorphic solutions of certain nonlinear partial differential equations in several complex variables involving differential and functional operators. Let $f$ be a non-constant meromorphic function in…
Common meadows are fields expanded with a total inverse function. Division by zero produces an additional value denoted with "a" that propagates through all operations of the meadow signature (this additional value can be interpreted as an…
We give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of…
The space of linear differential operators on a smooth manifold $M$ has a natural one-parameter family of $Diff(M)$ (and $Vect(M)$)-module structures, defined by their action on the space of tensor-densities. It is shown that, in the case…