Related papers: A note on partial polynomial functions, in memory …
We study a question on characterizing polynomials among rational functions of degree $>1$ on the projective line over an algebraically closed field that is complete with respect to a non-trivial and non-archimedean absolute value, from the…
In this paper we present a proof of Hartogs' extension theorem, following T. Sobieszek's paper from 2003. Hartogs' theorem provides a large class of domains where holomorphic functions have analytic continuation to larger domains, and is "a…
In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…
By restricting the variables running over various (possibly different) subfields, we introduce the notion of a partial zeta function. We prove that the partial zeta function is rational in an interesting case, generalizing Dwork's well…
The notion of monogenic (or regular) functions, which is a correspondence of holomorphic functions, has been studied extensively in hypercomplex analysis, including quaternionic, octonionic, and Clifford analysis. Recently, the concept of…
We introduce the notion of characteristic function of a quaternionic matrix, whose roots are the left eigenvalues. We prove that for all $2\times 2$ matrices and for $3\times 3$ matrices having some zero entry outside the diagonal there is…
In this paper we give simple extension and uniqueness theorems for restricted additive and logarithmic functional equations.
Using the theory of functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of $q$-partial differential equations, then, it can be expanded in terms of the product of the…
We introduce the notion of "quasi-symmetric" polynomials, which is a generalization of the notion of symmetry, and is particularly suited to the setting of polynomial rings over finite fields. The properties of this new class of functions…
The purpose of this paper is to obtain some sufficient conditions to determine the relation between a meromorphic function and an L-function when certain differential polynomial generated by them sharing a one degree polynomial. The main…
We give positive answer to a conjecture by Agranovsky. A continuous function on the sphere which has separate holomorphic extension along the set of complex lines passing through three non aligned interior points, is the trace of a…
In this paper, we prove some uniqueness results which improve and generalize several earlier works. Also, we prove a value distribution result concerning $f^{(k)}$ which provides a partial answer to a question of Fang and Wang [A note on…
The paper proposes a vector generalization of the basic concepts of the theory of complex variable: the concept of modulus and argument of complex number. The author introduces some generalizations of the notion of holomorphic functions and…
Let $f$ be a real polynomial of $x = (x_1,\dots,x_n)$ and $\varphi$ be a locally integrable function of $x$ which satisfies a holonomic system of linear differential equations. We study the distribution $f_+^\lambda\varphi$ with a…
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
Motivated by the general problem of extending the classical theory of holomorphic functions of a complex variable to the case of quater- nion functions, we give a notion of an H-derivative for functions of one quaternion variable. We show…
In the paper, we investigate the uniqueness problem of a power of an entire function that share one value partially with it's linear differential polynomial and obtain a result, which improves several previous results in a large scale. Also…
System of alternatively orthogonalized rational functions of Jacobi type on the half line $[1, \infty)$ is defined and its properties are established. Three subsystems of proper and mixed systems of rational functions with nice properties…
This paper is devoted to the uniqueness problem of the power of a meromorphic function with its differential polynomial sharing a set. Our result will extend a number of results obtained in the theory of normal families. Some questions are…
We generalize Chirka's theorem on the extension of functions holomorphic in a neighbourhood of graph(F)\cup(\partial D\times D) -- where D is the open unit disc and graph(F) denotes the graph of a continuous D-valued function F -- to the…