Related papers: Green's Functions of Recurrence Relations with Ref…
We continue the attempt to develop a theory of character sheaves on a not necessarily connected reductive algebraic group. In this paper we introduce and study the generalized Green functions.
The properties of the Wilson rational functions ${}_{10}\phi_9$ with three different normalizations are described. For one normalization, it satisfies an $R_{II}$ recurrence relation, whereas for the two other ones, they satisfy a…
We model generalized harmonic functions on rings of differential operators and complex function spaces. The differential operators in the second Weyl-algebra that commute with rotations are described and leads to a natural notion for such…
In this work, Miller Ross function with bicomplex arguments has been introduced. Various properties of this function including recurrence relations, integral representations and differential relations are established. Furthermore, the…
Given a sequence of regular planar domains converging in the sense of kernel, we prove that the corresponding Green's functions converge uniformly on the complex sphere, provided the limit domain is also regular, and the connectivity is…
Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain simple representations for the Green's function of the Dirac-Oscillator and Dirac-Coulomb problems. This is accomplished…
Partial differential equations are often used to model various physical phenomena, such as heat diffusion, wave propagation, fluid dynamics, elasticity, electrodynamics and image processing, and many analytic approaches or traditional…
We consider some bilinear recurrences that have applications in number theory. The explicit solution of a general three-term bilinear recurrence relation of fourth order is given in terms of the Weierstrass sigma function for an associated…
New differential-recurrence properties of dual Bernstein polynomials are given which follow from relations between dual Bernstein and orthogonal Hahn and Jacobi polynomials. Using these results, a fourth-order differential equation…
For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…
Arakelov-Green functions defined on metrized graphs have important role in relating arithmetical problems on algebraic curves into graph theoretical problems. In this paper, we clarify the combinatorial interpretation of certain…
A new density matrix and corresponding quantum kinetic equations are introduced for fermions undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). A central element in our derivation…
We study Green functions for stationary Stokes systems satisfying the conormal derivative boundary condition. We establish existence, uniqueness, and various estimates for the Green function under the assumption that weak solutions of the…
The paper is devoted to a generalization of static and dynamic mathematical models of behavior with explicitly stated reflexive models of agents' decision-making. Reflexion is considered as agent's beliefs about nature, opponents' beliefs…
We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication…
Consider a sequence of real-valued functions of a real variable given by a homogeneous linear recursion with differentiable coefficients. We show that if the functions in the sequence are differentiable, then the sequence of derivatives…
We study nonlocal integral equations on bounded domains with finite-range nonlocal interactions that are localized at the boundary. We establish a Green's identity for the nonlocal operator that recovers the classical boundary integral,…
A correspondence between arbitrary Fourier series and certain analytic functions on the unit disk of the complex plane is established. The expression of the Fourier coefficients is derived from the structure of complex analysis. The…
We present a further development of methods for analytical calculations of Green's functions of lattice fermions based on recurrence relations. Applying it to tight-binding systems and topological superconductors in different dimensions we…
Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the…