Hermite-Poulain Theorems for Linear Finite Difference Operators [PDF]
Constructive Approximation, 2020 We establish analogues of the Hermite-Poulain theorem for linear finite difference operators with constant coefficients defined on sets of polynomials with roots on a straight line, in a strip, or in a half-plane. We also consider the central finite difference operator of the form $$ Δ_{θ, h}(f)(z)=e^{iθ}f(z+ih)-e^{-iθ}f(z-ih), \quadθ\in[0,π),\ \ h\in ...
Mikhail Tyaglov, Anna Vishnyakova
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Spectrum of Linear Difference Operators and the Solvability of Nonlinear Discrete Problems [PDF]
Discrete Dynamics in Nature and Society, 2010 Let T∈ℕ with T>5. Let 𝕋:={1,…,T}. We study the Fučik spectrum Σ of the discrete problem Δ2u(t-1)+λu+(t)-μu-(t)=0, t∈𝕋, u(0)=u(T+1)=0, where u+(t)=max{u(t),0}, u-(t)=max{-u(t),0}.
Ruyun Ma, Youji Xu, Chenghua Gao
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Reducible linear difference operators
Aequationes Mathematicae, 1972 Let \(f = \sum_{i=0}^n A^{(i)}y_i\), \(A^{(n)}\ne 0\), be a linear homogeneous difference polynomial (LHDP) with coefficients in the difference field \(k\) of characteristic 0. The author defines \(f\) to be reducible at \(q\) to order \(r\), \(r 2\) there exists a class of second order difference equations reducible at \(q\) but not at any \(t1 ...
Charles H Franke, Franke Charles H
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Linear perturbations of differential of difference operators with polynomials as eigenfunctions
Journal of Computational and Applied Mathematics, 1997 Let the polynomials \(\{P_n(x)\}^\infty_{n=0}\) with \(\deg P_n=n\) be eigenfunctions of a linear differential or difference operator \(L\) with eigenvalues \(\{\lambda_n\}^\infty_{n=0}\). In this paper, necessary and sufficient conditions are given for the polynomials \(\{Q_n(x)\}^\infty_{n=0}\) such that the polynomials \(\{P_n(x)+\mu Q_n(x ...
H Bavinck
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The Algebra of Linear Partial Difference Operators and Its Applications [PDF]
SIAM Journal on Mathematical Analysis, 1980 The algebra of linear partial difference operators is investigated, and an elimination procedure demonstrated. Applications to combinatorics are given. In particular, a new proof and a q-analogue of MacMahon’s Master Theorem are given.
Doron Zeilberger
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Differences of Positive Linear Operators on Simplices [PDF]
Journal of Function Spaces, 2021 The aim of the paper is twofold: we introduce new positive linear operators acting on continuous functions defined on a simplex and then estimate differences involving them and/or other known operators. The estimates are given in terms of moduli of smoothness and K ...
Ana-Maria Acu +2 more
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Linear isomorphic spaces of fractional-order difference operators
Alexandria Engineering Journal, 2021 In the present paper, we intend to make an approach to introduce and study the applications of fractional-order difference operators by generating Orlicz almost null and almost convergent sequence spaces.
S.A. Mohiuddine +3 more
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Calculation of particular solutions of nonhomogeneous linear equations with two linear operators, of which at least one is almost algebraic, in the case of simple roots of the characteristic equation [PDF]
Компьютерные исследования и моделирование, 2016 The concept of an operator is an almost algebraic with respect to two-sided ideal of the algebra of linear operators in some finite-dimensional linear spaces, it extended to the case when the ideal is left.
Vladimir G. Tsirulik
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Methods for image noise level estimation
Компьютерная оптика, 2021 The article presents a method for estimating the level of discrete white noise in an image, based on the use of linear difference operators with a vector mask.
A.I. Novikov, A.V. Pronkin
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Linearly reducible linear difference operators
Aequationes Mathematicae, 1971 Charles H Franke, Franke Charles H
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