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With the help of the notion of weighted sharing of sets, this paper dealt with the question posed by \emph{Yi} \cite{Yi-SC-1994} regarding the uniqueness of meromorphic functions concerning three set sharing. A result has been proved which…
We first exhibit counterexamples to some open questions related to a theorem of Sakai. Then we establish an extension theorem of Sakai type for separately holomorphic/meromorphic functions.
The first-order Euler-Maclaurin formula relates the sum of the values of a smooth function on an interval of integers with its integral on the same interval on $\mathbb R$. We formulate here the analogue for functions that are just of…
We consider the index problem for a wide class of nonlocal elliptic operators on a smooth closed manifold, namely differential operators with shifts induced by the action of an isometric diffeomorphism. The key to the solution is the method…
We classify self-adjoint first-order differential operators on weighted Bergman spaces on the unit disc and answer questions related to uncertainty principles for such operators. Our main tools are the discrete series representations of…
In this paper we would like to show the interrelation between the different mathematical theories concerning the Schur interpolation problem, contractions in Hilbert spaces, pseudocontinuation and Darlington synthesis. The main objects of…
We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion…
In this paper, we introduce new spaces of holomorphic functions on the unit ball $\mathbb{B}_{n}$ of $\mathbb{C}^{n}$ generalizing the classical Bergman spaces. The main results include the properties of some operators and integrals…
We introduce a notion of resultant of two meromorphic functions on a compact Riemann surface and demonstrate its usefulness in several respects. For example, we exhibit several integral formulas for the resultant, relate it to potential…
The maximum of the modulus of a meromorphic function cannot be restricted from above by the Nevanlinna characteristic of this meromorphic function. But integrals from the logarithm of the module of a meromorphic function allow similar…
We consider the $n{\times}n$ matrix linear differential systems in the complex plane. We find necessary and sufficient conditions under which these systems have meromorphic fundamental solutions. Using the operator identity method we…
It is shown that a separated sequence of points in the unit disc of the complex plane is in fact uniformly separated, if there exists a certain intermediate sequence whose separated subsequences are uniformly separated. This property is…
We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are ``open-string-theoretic,'' ``noncommutative'' generalizations of the notions of vertex algebra and of…
The operad of moulds is realized in terms of an operational calculus of formal integrals (continuous formal power series). This leads to many simplifications and to the discovery of various suboperads. In particular, we prove a conjecture…
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.
This paper makes a modest contribution to the family of starlike univalent mappings in the open unit disk, by the introduction of some new subclasses of them via certain convolution operators. A new univalence condition is given with…
We consider the class $\Sigma(p)$ of univalent meromorphic functions $f$ on $\ID$ having simple pole at $z=p\in[0,1)$ with residue 1. Let $\Sigma_k(p)$ be the class of functions in $\Sigma(p)$ which have $k$-quasiconformal extension to the…
We study noncommutative versions of holomorphic and harmonic functions on the unit disk.
We consider various systematic ways of defining unbounded operator valued integrals of complex functions with respect to (mostly) positive operator measures and positive sesquilinear form measures, and investigate their relationships to…
Operator-valued multivariable Bohr type inequalities are obtained for: a class of noncommutative holomorphic functions, generalizing the analytic functions on the open unit disc; the noncommutative disc algebra and the noncommutative…