Related papers: Higher-order interlacing for matrix-valued meromor…
In this paper, we investigate shared value problems for shifts and higher-order difference operators of meromorphic and entire functions in several complex variables. Using Nevanlinna theory in $\mathbb{C}^n$, we obtain new uniqueness…
Our starting point is a basic problem in Hermite interpolation theory, namely determining the least degree of a homogeneous polynomial that vanishes to some specified order at every point of a given finite set. We solve this problem if the…
This current article aims to study a new subclass of meromorphic functions with positive coefficients by reconstructing a new operator in the punctured open disc. Also, some geometric properties are considered and investigated, such results…
We consider the problem of interpolating a function given on scattered points using Hermite-Birkhoff formulas on the sphere and other manifolds. We express each proposed interpolant as a linear combination of basis functions, the…
In connection with the Herglotz-Nevanlinna integral representation of so-called Pick functions, we introduce the notion of boundary measure of holomorphic functions on the imaginary domain and elucidate some of basic properties.
We consider the reproducing kernel function of the theta Bargmann-Fock Hilbert space associated to given full-rank lattice and pseudo-character, and we deal with some of its analytical and arithmetical properties. Specially, the…
We consider multiple orthogonal polynomials corresponding to two Macdonald functions (modified Bessel functions of the second kind), with emphasis on the polynomials on the diagonal of the Hermite-Pad\'e table. We give some properties of…
The paper deals with particular classes of $q\times q$ matrix-valued functions which are holomorphic in $\mathbb{C}\setminus[\alpha,+\infty)$, where $\alpha$ is an arbitrary real number. These classes are generalizations of classes of…
In this paper, subordination results are studied for certain subclass of p-valent meromorphic functions in the punctured unit disc having a pole of order p at the origin. The subclass under investigation is defined by using certain new…
We show that integrals involving log-tangent function, with respect to certain square-integrable functions on $(0, \pi/2)$, can be evaluated by some series involving the harmonic number. Then we use this result to establish many closed…
We prove an analogue for trees of Courant's theorem on the interlacing property of zeros of eigenfunctions of a Schr\"{o}dinger operator. Let $\Gamma$ be a finite tree, and $\mathcal A$ a Schr\"{o}dinger operator on $\Gamma$. If the…
In this paper the analytic characterization of generalized poles of operator valued generalized Nevanlinna functions (including the length of Jordan chains of the representing relation) is completed. In particular, given a Jordan chain of…
To a function with values in the power set of a pre-ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre-Fenchel conjugate for set-valued…
We show that it is possible to approximate the zeta-function of a curve over a finite field by meromorphic functions which satisfy the same functional equation and moreover satisfy (respectively do not satisfy) the analogue of the Riemann…
We generalize our earlier results from \cite{K} on the Bessmertny\u{\i} class of operator-valued functions holomorphic in the open right poly-halfplane which admit representation as a Schur complement of a block of a linear homogeneous…
We study meromorphic functions in a strip almost periodic with respect to the spherical metric. Then we get a complete description of zeros and poles for this class of functions, find a condition for a meromorphic almost periodic function…
In this paper, we establish some new inequalities of the Hermite-Hadamard like for class of (h-s)_{1,2}-convex functions which are ordinary, super-multiplicative or similarly ordered and nonnegative.
A definition of hyperbolic meromorphic functions is given and then we discuss the dynamical behavior and the thermodynamic formalism of hyperbolic functions on the Julia set. We prove the important expanding properties for hyperbolic…
New classes of generalized Nevanlinna functions, which under multiplication with an arbitrary fixed symmetric rational function remain generalized Nevanlinna functions, are introduced. Characterizations for these classes of functions are…
We prove nonlinear relation on multiple Hurwitz-Riemann zeta functions. Using analytic continuation of these multiple Hurwitz-Riemann zeta function, we quote at negative integers Euler's nonlinear relation for generalized Bernoulli…