-smoothness of invariant fiber bundles for dynamic equations on measure chains.
A class of infinite series including terms of generalized sequences.
A Levy-Khinchin Formula for Semigroups with Involutions.
A proof of a conjecture by Karamata.
A proof of Leibniz's formula for divided differences.
Addendum to the article: Polylogarithms in the field of omega (a root of a given cubic): Functional equations and ladders.
An Apéry-like difference equation for Catalan's constant.
Analog of Favard's Theorem for Polynomials Connected with Difference Equation of 4-th Order
Orthonormal polynomials on the real line {pn (λ)} n=0 ... ∞ satisfy the recurrent relation of the form: λn−1 pn−1 (λ) + αn pn (λ) + λn pn+1 (λ) = λpn (λ), n = 0, 1, 2, . . . , where λn > 0, αn ∈ R, n = 0, 1, . . . ; λ−1 = p−1 = 0, λ ∈ C. In this paper we study systems of polynomials {pn (λ)} n=0 ... ∞ which satisfy the equation: αn−2 pn−2 (λ) + βn−1 pn−1 (λ) + γn pn (λ) + βn pn+1 (λ) + αn pn+2 (λ) = λ2 pn (λ), n = 0, 1, 2, . . . , where αn > 0, βn ∈ C, γn ∈ R, n = 0, 1, 2, . . ., α−1 = α−2...
Asymptotical behaviors of nonautonomous discrete Kolmogorov system with time lags.
Basic concepts of the difference geometry
Characterization of a class of functions using divided differences.
Conservation laws of discrete Korteweg-de Vries equation.
Covering systems, Kubert identities and difference equations
Difference independence of the Riemann zeta function
Distribution of zeros and shared values of difference operators
We investigate the distribution of zeros and shared values of the difference operator on meromorphic functions. In particular, we show that if f is a transcendental meromorphic function of finite order with a small number of poles, c is a non-zero complex constant such that for n ≥ 2, and a is a small function with respect to f, then equals a (≠ 0,∞) at infinitely many points. Uniqueness of difference polynomials with the same 1-points or fixed points is also proved.
Ein Beitrag zur Differenzrechnung und zur Zahlentheorie.
Eine Anwendung der Differenzengleichungen in der theoretischen Statistik
Équations aux différences associées à des groupes, fonctions représentatives.
Inspiré par un travail de J.-P. Bézivin et F. Gramain sur les systèmes d’équations aux différences, on caractérise les sous-groupes d’un groupe de Lie réel (resp. complexe) , pour lesquels toute fonction continue (resp. entière) telle que l’ensemble des -translatées engendrent un -espace vectoriel de dimension finie, engendrent aussi un -espace vectoriel de dimension finie par - translation. On fait le lien avec les systèmes d’équations aux différences à coefficients constants.
Étude sur les équations fonctionnelles
Existence and positivity of solutions for a nonlinear periodic differential equation
We study the existence and positivity of solutions of a highly nonlinear periodic differential equation. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ a modification of Krasnoselskii’s fixed point theorem introduced by T. A. Burton ([4], Theorem 3) to show the existence and positivity of solutions of the equation.