Showing papers in "Journal of Approximation Theory in 2003"

TL;DR: It is proved that for a function f analytic in {z: |z| < q + e} the rate of convergence of {Bn(f, q; x)} to f(x) in the norm of C[0,1] has the order q-n (versus 1/n for the classical Bernstein polynomials).

TL;DR: The concept of a canonical mask for a given matrix mask is introduced and by investigating several properties of the initial function vectors in a vector cascade algorithm, a relatively unified approach is taken to study several questions such as convergence, rate of convergence and error estimate for a perturbed mask of avector cascade algorithm in a Sobolev space.

TL;DR: The pointwise limit S of a sequence of Stieltjes transforms of real Borel probability measures is itself the Sti Beltjes transform of a Borel p.m.

TL;DR: This work establishes q-analogues of Taylor series expansions in special polynomial bases for functions analytic in bounded domains and for entire functions whose maximum modulus M(r;f) satisfies |ln M( r;f)|≤A ln2r.

TL;DR: Using the steepest descent method of Deift and Zhou, this work analyses the Riemann-Hilbert problem, and obtains complete asymptotic expansions of the recurrence coefficients of orthogonal polynomials associated to the generalized Jacobi weight.

TL;DR: Two classes of Jacobi matrix operators in l2 with zero diagonals and with weights of the form nα + cn for 0 1 are considered, where {cn} is periodic.

TL;DR: The aim of this paper is to discuss the L1 case and prove for f ∈ L1(Gm) that the relation σMnf → f holds a.e. (Mn is the nth generalized power).

TL;DR: Averages on the sphere aboutx in Rd and on the rim of the cap about x in Sd-1 and their iterates are shown to be smoother than f and their approximating properties satisfy a strong converse inequality of type A when dealing with multivariate approximation.

TL;DR: The properties of Pn(WrQ2;x), which contain extensions of Levin and Lubinsky's results and improvements of Bauldry's results, are investigated.

TL;DR: The notion of bilinear moment functional is introduced as a generalization of the corresponding notion for moment functionals and motivated by the applications to multi-matrix random models.

TL;DR: A strengthened general inequality of the Hardy-Knopp type is proved and its dual inequality is derived and the obtained results are applied to unify the strengthened classical Hardy and Polya-K nopp's inequalities deriving them as special cases of the obtained general relations.

TL;DR: The generalized Riesz means, which were introduced by Ditzian (Acta Math.

TL;DR: The purpose of the article is to study how to apply a basic Borel-Laplace transformation to q-difference equations satisfied by the q-Bessel functions of F.H. Jackson.

TL;DR: It is given sufficient conditions for the universality of tensor products of sequences of operators defined on Frechet spaces when the tensor product T ~ R of two operators is chaotic in the sense of Devaney.

TL;DR: Representations for the Riesz kernel | x-y | - s are presented, which lead to new interpretations of the energy of measures, and it is shown that the surface measure on the unit sphere in R d solves a minimal energy problem independent of s (but intimately related to RiesZ s -energy).

TL;DR: Using a factorization method, the poisedness of a Hermite interpolation based on points located on various circles, not necessarily concentric, is established, which gives many new sets of poised interpolation points.

TL;DR: It is shown that the general approximation property of feed-forward multilayer perceptron networks can be achieved in networks where the number of nodes in each layer is bounded, but the numberof layers grows to infinity.

TL;DR: It is shown that under suitable conditions on u and v, lim supn → ∞ n1/2 |λp-1/p ∫ab |u(t)v(t)|dt - nan(T)| ≤ c(||u'||p'/(p'+1) + ||v'|| p/(p+1), where ||w||p is the first eigenvalue of the p-Laplacian eigen value problem on (0

TL;DR: A generalisation of the multivariate beta integral is given and it follows that this operator inherits many properties of the Bernstein-Durrmeyer operator in a natural way and is determined its eigenstructure and given a differentiation formula for it which is new.

TL;DR: A modification of Dykstra's algorithm which allows us to avoid projections onto general convex sets and to calculate projections onto either a half-space or onto the intersection of two half-spaces is presented.

TL;DR: It is proved that the independence of the asymptotic behavior of the entropy numbers ek(id : RBp0,q0s0(Rn) ↦ RBs1p1,q1( Rn) from the difference s0 - s1 as long as the embedding itself RBs0p0-q0(rn) → RBs2p1-q1 (Rn), is compact.

TL;DR: It is proved that the (C, δ;) means of any continuous function converge uniformly in the norm of C(Sd-1) if and only if δ > (d - 2)/2 + Σj=1d kj -- min1 ≤ j ≤ d kj.

TL;DR: It is proved that the Sobolev orthogonal polynomials with respect to the measure µ have the same asymptotic behaviour as well as the Fourier series associated to this inner product provided that µ is the Jacobi measure.

TL;DR: It is proved that if f ∈ Cw([0, 1]2) and the function f is bounded partial p- variation for some p ∈ [1, + ∞) then the double Walsh-Fourier series of thefunction f is uniformly (C;-α,β) summable (α + β 0) in the sense of Pringsheim.

TL;DR: The asymptotic behavior of quadratic Hermite-Pade polynomials pn, qn, rn ∈ Pn associated with the exponential function is studied and analytic expressions are proved that form the basis for the investigation of the convergence of four-way approximants.

TL;DR: In this paper, a multinode higher order expansion of a function is presented, where the error terms of the expansions are given by using the values and higher derivatives of the function at the given nodes.

TL;DR: A unified approach to convergence rates for many particular strongly continuous solution families associated to linear evolution equations such as the abstract Cauchy problem of the first and second order, and integral Volterra equations of convolution type is provided.

TL;DR: In this paper, it was shown that the approximation of the embedding operator of the Sobolev space L 1,p(G) on a graph G of finite length |G| into the space L p(G,µ, where µ is an arbitrary finite Borel measure on G, satisfy the inequality an≤|G|1/p' µ(G), 1/pn-1, 1 < p < ∞.

TL;DR: It is shown that an iterative numerical algorithm for computing the ratios and products of complete integrals has the second order of convergence.

TL;DR: In this paper, the orthonormal polynomials associated to a measure dµ of compact support in R were shown to have at most one zero in (E − δ, E + δ).