Related papers: Linear Delay-Differential operator of a meromorphi…
In this article, we prove a normality criterion for a family of meromorphic functions which involves sharing of holomorphic functions. Our result generalizes some of the results of H. H. Chen, M. L. Fang and M. Han, Y. Gu.
We treat shared value problems for rational functions $R(z)$ and their derivative $R'(z)$ in the plane and on the sphere. We also consider shared values for the pair $R(w)$ and $\partial_{z} R = \lambda w \cdot R'(w)$ on ${\mathbb C}…
We use the embedding formalism to study correlation functions of a d-dimensional Euclidean CFT in the presence of a $q$ co-dimensional defect. The defect breaks the global conformal group $SO(d+1,1)$ into $SO(d-q+1,1) \times SO(q)$. We…
We show that the method of separation of variables gives a natural generalisation of integral relations for classical special functions of one variable. The approach is illustrated by giving a new proof of the ``quadratic'' integral…
In this paper, we study the cooperative output regulation problem for the discrete linear time-delay multi-agent systems by distributed observer approach. In contrast with the same problem for continuous-time linear time-delay multi-agent…
Given an entire function $f$ of finite order $\rho$, let $L(z,f)=\sum_{j=0}^{m}b_{j}(z)f^{(k_{j})}(z+c_{j})$ be a linear delay-differential polynomial of $f$ with small coefficients in the sense of $O(r^{\lambda+\varepsilon})+S(r,f)$,…
In 2023 in (3), Uwe finds the explicit form of the map which is which is settled in ZN of finite functional degree and14 discusses how to compute its usual degree w.r.t to the derivative in the linear form, i.e. the product of ones formed…
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
Classical prolate spheroidal functions play an important role in the study of time-band limiting, scaling limits of random matrices, and the distribution of the zeros of the Riemann zeta function. We establish an intrinsic relationship…
The space of m-ary differential operators acting on weighted densities is a (m+1)-parameter family of modules over the Lie algebra of vector fields. For almost all the parameters, we construct a canonical isomorphism between this space and…
The Mittag-Leffler function plays an important role in Geometric Function Theory, particularly in the study of analytic and meromorphic function classes. Among its various generalizations, the Barnes-Mittag-Leffler function stands out due…
In this article we develop a general technique which takes a known characterization of a property for weighted backward shifts and lifts it up to a characterization of that property for a large class of operators on $L^p(X)$. We call these…
In [1], an operator was introduced which acts parallel to the Riemann-Liouville differintegral on a transformation of the space of real analytic functions and commutes with itself. This paper aims to extend the technique - and its defining…
This paper is mostly a survey, with a few new results. The first part deals with functional equations for q-exponentials, q-binomials and q-logarithms in q-commuting variables and more generally under q-Heisenberg relations. The second part…
Q-Learning is a fundamental off-policy reinforcement learning (RL) algorithm that has the objective of approximating action-value functions in order to learn optimal policies. Nonetheless, it has difficulties in reconciling bias with…
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…
Yang-Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with…
This is a continuation of the paper (quant-ph/0009012). In this letter we extend coherent operators and study some basic properties (the disentangling formula, resolution of unity, commutation relation, etc). We also propose a perspective…
In this note, we present a characterization of semistable unitary operators on $L^2(\mathbb{R})$, under the assumption that the operator is (i) translation-invariant, (ii) symmetric, and (iii) locally uniformly continuous (LUC) under…
We study canonical systems that are reflectionless on an open set. In this situation, the two half line $m$ functions are holomorphic continuations of each other and may thus be combined into a single holomorphic function. This idea was…