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We introduce a \emph{q}-differential operator adapted to \emph{q}-spinor variables, establishing a corresponding \emph{q}-spinor chain rule and defining both standard and Dirac-type \emph{q}-differential operators. Integral formulas in…
The paper gives a precise asymptotic relation between higher order logarithmic difference and logarithmic derivatives for meromorphic functions with order strictly less then one. This allows us to formulate a useful Wiman-Valiron type…
We study decentralized designing of the graph shift operators to implement linear transformations between graph signals. Since this operator captures the local structure of the graph, the proposed method of this paper gives rise to…
In this paper, we establish a new second main theorem for meromorphic functions on a non-Archimedean field and small functions with counting functions truncated to level $1.$ As an application, we show that two meromorphic functions on a…
We consider systems of linear differential and difference equations \begin{eqnarray*} \partial Y(x) =A(x)Y(x), \sigma Y(x) =B(x)Y(x) \end{eqnarray*} with $\partial = \frac{d}{dx}$, $\sigma$ a shift operator $\sigma(x) = x+a$, $q$-dilation…
We determine all pairs $(f,g)$ of meromorphic functions that share four pairs of values $(a_\nu,b_\nu)$, $1\le\nu\le 4$, and a fifth pair $(a_5,b_5)$ under some mild additional condition.
We study some classes of symmetric operators for the discrete series representations of the quantum algebra U_q(su_{1,1}), which may serve as Hamiltonians of various physical systems. The problem of diagonalization of these operators…
We propose a delayed Mittag-Leffler type matrix function with logarithm, which is an extension of the classical Mittag-Leffler type matrix function with logarithm and delayed Mittag-Leffler type matrix function. With the help of the delayed…
We investigate the meromorphic quasi-modular forms and their $L$-functions. We study the space of meromorphic quasi-modular forms. Then we define their $L$-functions by using the technique of regularized integral. Moreover, we give an…
The objective of this study is to ascertain the existence and forms of the finite order meromorphic and entire functions of several complex variables satisfying some certain Fermat-type partial differential-difference equations by…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
Thirty research questions on meromorphic functions and complex differential equations are listed and discussed. The main purpose of this paper is to make this collection of problems available to everyone.
In this paper we have studied the growth of meromorphic solutions of higher order homogeneous and non-homogeneous linear difference equations with entire and meromorphic coefficients. We have extended and improved some results of Zhou and…
Consider an elliptic self-adjoint pseudodifferential operator $A$ acting on $m$-columns of half-densities on a closed manifold $M$, whose principal symbol is assumed to have simple eigenvalues. We show existence and uniqueness of $m$…
We study linear recurrence relations in the character solutions of $Q$-systems obtained from the Kirillov-Reshetikhin modules. We explain how known results on difference $L$-operators lead to a uniform construction of linear recurrences in…
In this paper, we employ the theory of normal families in several complex variables to obtain some uniqueness theorems for entire functions. These results extend the related works of Li and Yi [11], and Lu et al. [18] to the setting of…
We revisit and connect several notions of algebraic multiplicities of zeros of analytic operator-valued functions and discuss the concept of the index of meromorphic operator-valued functions in complex, separable Hilbert spaces.…
The aim of the article is to prove $L^{p}-L^{q}$ off-diagonal estimates and $L^{p}-L^{q}$ boundedness for operators in the functional calculus of certain perturbed first order differential operators of Dirac type for with $p\le q$ in a…
Exchange of crucial and confidential information leads to the unprecedented attention on the security problem in wireless networks. Though the security has been studied in a number of works, the joint optimization of the physical layer…
For two meromorphic functions $ f $ and $ g $, the equation $ f^m+g^m=1 $ can be regarded as Fermat-type equations. Using Nevanlinna theory for meromorphic functions in several complex variables, the main purpose of this paper is to…