The aim of the paper is to get an estimation of the error of the general interpolation rule for functions which are real valued on the interval $[-a,a]$, $a\in (0,1)$, have a holomorphic extension on the unit circle and are quadratic integrable on the boundary of it. The obtained estimate does not depend on the derivatives of the function to be interpolated. The optimal interpolation formula with mutually different nodes is constructed and an error estimate as well as the rate of convergence are obtained. The general...

In questa nota, si studiano problemi di interpolazione per varietà discrete in spazi di funzioni olomorfe in coni. In particolare si mostra come sia possibile estendere il Principio Fondamentale di Ehrenpreis ad equazioni di convoluzione nella spazio $H_c(\mathrm{\Omega })$, introdotto in [4] in connessione con problemi di fisica quantistica.

Si estendono qui i risultati della nota precedente al caso di varietà non discrete. Ciò viene utilizzato per ottenere un teorema di rappresentazione per soluzioni di sistemi di equazioni di convoluzione in spazi di funzioni olomorfe in coni.

On démontre un résultat concernant l’interpolation de fonctions analytiques sur une perturbation d’ensemble produit qui, dans le cas $p$-adique, répond à une conjecture de P.Robba et, dans le cas complexe, complète des résultats antérieurs de E.Bombieri, S.Lang, D.Masser, J.-C.Moreau et M.Waldschmidt.

We establish an interpolation theorem for a class of nonlinear operators in the Lebesgue spaces ${ℒ}^s\left(ℝⁿ\right)$ arising naturally in the study of elliptic PDEs. The prototype of those PDEs is the second order p-harmonic equation ${div\left|\nabla u\right|}^{p-2\nabla }u=div$. In this example the p-harmonic transform is essentially inverse to $div\left(\right|\nabla {|}^{p-2}\nabla )$. To every vector field $\in {ℒ}^q(ℝⁿ,ℝⁿ)$ our operator ${\mathscr{H}}_p$ assigns the gradient of the solution, ${\mathscr{H}}_p=\nabla u\in {ℒ}^p(ℝⁿ,ℝⁿ)$. The core of the matter is that we go beyond the natural domain of definition of this operator. Because of nonlinearity our arguments...

We establish results on invariant approximation for fuzzy nonexpansive mappings defined on fuzzy metric spaces. As an application a result on the best approximation as a fixed point in a fuzzy normed space is obtained. We also define the strictly convex fuzzy normed space and obtain a necessary condition for the set of all $t$-best approximations to contain a fixed point of arbitrary mappings. A result regarding the existence of an invariant point for a pair of commuting mappings on a fuzzy metric...

Les valeurs aux entiers pairs (strictement positifs) de la fonction $\zeta$ de Riemann sont transcendantes, car ce sont des multiples rationnels de puissances de $\pi$. En revanche, on sait très peu de choses sur la nature arithmétique des $\zeta (2k+1)$, pour $k\ge 1$ entier. Apéry a démontré en 1978 que $\zeta \left(3\right)$ est irrationnel. Rivoal a prouvé en 2000 qu’une infinité de $\zeta (2k+1)$ sont irrationnels, mais sans pouvoir en exhiber aucun autre que $\zeta \left(3\right)$. Il existe plusieurs points de vue sur la preuve d’Apéry ; celui des séries hypergéométriques...

An isomorphism between some anisotropic Besov and sequence spaces is established, and the continuity of a Stieltjes-type integral operator, acting on some of these spaces, is proved.

In this paper we are concerned with a general class of positive linear operators of discrete type. Based on the results of the weakly Picard operators theory our aim is to study the convergence of the iterates of the defined operators and some approximation properties of our class as well. Some special cases in connection with binomial type operators are also revealed.