Showing papers in "Journal of Approximation Theory in 1985"

TL;DR: In this article, the authors considered the resistance of materials to certain types of deformations, and introduced the space of functions of bounded mean oscillation (BMO) and the John-Nirenberg inequality.

TL;DR: In this article, the authors studied the convergence of Bernstein-type polynomial operators defined for integrable functions on a simplex T in R' in the context of simplex integrability.

TL;DR: In this paper, sufficient conditions for the existence of a bounded interpolating projection onto subspaces of C[0, 1] are found, and for spaces of piecewise polynomial functions the projection can be bounded by the B-spline basis condition number.

TL;DR: In this article, strong approximation of Fourier series is shown to be the best possible refinement of an inequality of L. Leindler, which is related to the inverse problem.

TL;DR: In this article, a localization theorem for β approximation operators β n (n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 26, 28, 30, 31, 34, 35, 36, 34) was proved for β n ǫ to β nǫ for every fixed interval [X 1, x 2 ] (0 x 1 ⩽ x 2 ], where x >

TL;DR: In this paper, a sous-ensemble compact de C tel que C-X a un nombre fini de composantes connexes is considered, and a sens faible peut etre uniformement approche sur X par des fonctions ψ satisfaisant ∂(∂ψ/∂g)=0 dans un voisinage de X who satisfait ∂g(z)¬=0 ∀z∈x.

TL;DR: In this article, sharp estimations for moments and moment-generating functions of suitable random variables are provided for exponential operators as well as a class of Poisson approximation theorems in probability theory.

TL;DR: In this article, it was shown that f has an (essentially) unique best L 1 -approximation f 1 by nondecreasing functions; f 1 is shown to be continuous.

TL;DR: In this paper, estimates for orthogonal polynomials associated with exp(− x m ), x real, m even, and exp( − x m ) are given.

TL;DR: In this paper, the Freud-Christoffel function is shown to have upper and lower bounds in the form λ n,p (W,j,x) = inf |PW| Lp(R) |P (j) (X)| where the infimum is taken over all polynomials P(x) of degree at most n − 1.

TL;DR: In this paper, the authors applied the method of averaging to study the reduced evolution of a quantum open system and derived successive approximate evolutions, and they were shown to be asymptotic to the exact evolution of the open system, under conditions which are satisfied in the case of a system coupled to a quasi-free reservoir.

TL;DR: In this article, a generalization of Montessus de Ballore's theorem for the multivariate case is presented. But this generalization does not address the problem of finding a Pade approximant that preserves many of the properties of the univariate Pade approximation.

TL;DR: In this article, it is shown that two of these representations do not hold in general, and an improved version is given which is more general than existing results, based on a number of new results concerning weak Markov systems which may be of independent interest.

TL;DR: In this paper, the behavior of the largest root of an Euler-Frobenius polynomial was investigated, which determines the convergence/divergence of a cardinal Lagrange spline series.

TL;DR: In this article, a general unified recurrence relation for a class of B -splines defined by certain constant coefficient operators is provided, and associated relations for polynomial, trigonometric, hyperbolic, and some particular Tchebycheffian B-splines are all covered as special cases.

TL;DR: Gilewicz and Leopold as mentioned in this paper considered the location of zeros of polynomials satisfying three-term recurrence relations with complex coefficients and established the first results.

TL;DR: In this article, the trace de Λ k (R) is defined as a sous-ensemble clos F de R en utilisant des polynomes d'interpolation.

TL;DR: In this article, the authors deal with quantitative extensions of the classical condensation principle of Banach and Steinhaus to arbitrary (not necessarily countable) families of operators and apply it to the sharpness of approximation processes.

TL;DR: In this article, the authors give a characterization of finite-dimensional subspaces of L p, 1 ⩽ p C 0 (T ) whose metric projections admit linear selections.

TL;DR: In this article, the convergence of Lj to the identity operator I is closely related to the weak convergence of a sequence of finite measure μj, to the unit (Dirac) measure δx0, x0 ϵ [a, b].

TL;DR: In this paper, the minimum norm problem of finding an element in the convex set nearest to a given element in a bounded function with uniform norm has been studied and the required Lipschitzian selection operators with smallest possible constants have been determined.

TL;DR: The location of the zeros of polynomials satisfying a three-term recurrence relation is studied in this paper, and new results are obtained for some cases where some of the coefficients are positive or merely real.