Showing papers in "Journal of Approximation Theory in 2002"

TL;DR: It is shown that in general these properties of the sequence {Bn(f, q; x)∞n=1} are essentially different from those in the classical case q=1.

TL;DR: A family of two-point quadrature formulae is considered and sharp estimates for the remainders under various regularity conditions are established and improved forms of certain integral inequalities due to Hermite and Hadamard, Iyengar, Milovanovi?

TL;DR: For a Jacobi matrix J on ?2(Z+) with Ju(n)=an?1u(n?1)+bnu( n)+anu(n+1), it is proved that E2(E2?4)1/2??n?bn?+4?n?an-1? and bounds on higher moments are proved.

TL;DR: A sharpened version of Carleman's inequality is proved and this result may also be seen as a generalization of a continuous variant of Carleton's inequality, which is usually referred to as Knopp's inequality.

TL;DR: Bounds for the approximation error are established in terms of the maximum separation distance of the collocation points, the order of the pseudodifferential operator, and the smoothness of the employed zonal kernel.

TL;DR: The objective is first to establish, using only the q -Jackson integral and the q-derivative, some properties of this function with proofs similar to the classical case; second to construct the associated q-Fourier analysis which will be used in a coming work to constructThe q-analogue of the Bessel-hypergroup.

TL;DR: In this paper, approximation properties of Cesaro-means with @[email protected]?(0, 1) of Walsh-Fourier series are established and it is shown that this condition cannot be improved in the case p=1.

TL;DR: The limit distribution of the zeros of polynomial solutions of a class of generalized Lam?

TL;DR: It is proved that, if the parameter 0 0, as the number of iterates M→∞, the iterates of the Boolean sum of Bnf converge to the interpolating polynomial for f at n+1 geometrically spaced nodes on [0, 1].

TL;DR: These results offer a generalization to arbitrary operators of several theorems by de Boor, Atteia, Sard and others, which hold for closed range operators.

TL;DR: It is proved that Lp(I,G) is N-simultaneously proximinal in Lp (I,E), the space of all p-Bochner integrable functions on the interval I=0,1 with values in E, 1?p?∞.

TL;DR: It is proved that these schemes are third order accurate and smoothness of the limit function generated by these linear schemes is proved by using the well-known smoothness criteria of the uniform linear four-point scheme.

TL;DR: This paper shows that one gets at least the known order for interpolation with a less smooth kernel that has W as its native space.

TL;DR: The set P of all probability measures ? on the unit circle T splits into three disjoint subsets depending on properties of the derived set of {|?n|2d?}n?0, denoted by Lim(?).

TL;DR: The asymptotic behavior of the integral kernel of the Dunkl transform, the so-called Dunkl kernel, when one of its arguments is fixed and the other tends to infinity either within a Weyl chamber of the associated reflection group, or within a suitable complex domain is studied.

TL;DR: The monotonicity of xn,k(?,β) as functions of ? and β, ?,β>?1, is investigated and Elbert and Siafarikas proved that fn(?)=(?+(2n2+1)/(4n+2))1/2 obeys this property.

TL;DR: Natural q-extensions of the Bernoulli and Euler polynomials, numbers, and the Riemann zeta function are discussed as a by-product.

TL;DR: It is shown that for any expansive, integer valued 2×2 matrix, there exists a (multi-)wavelet whose Fourier transform is compactly supported and smooth.

TL;DR: It is proved that certain lacunary Haar systems in L"1 are quasi-greedy basic sequences.

TL;DR: New asymptotic relations for the errors of approximation in Lp?1,1], 00, are established by the Lagrange interpolation polynomials at the Chebyshev nodes of the first and second kind by way of corollary of the Bernstein constant B?,p?limn?∞n?+1/p infck??x????k=0nmckxk?Lp? 1,1]

TL;DR: It is proved that if the one-sided directional derivative of the generalized distance function associated to G at x equals to 1 or -1, then the generalized nearest points to x from G exist.

TL;DR: The density of the polynomials in weighted Sobolev spaces on curves is proved and the conditions under which the spaces are complete for non-closed compact curves are found.

TL;DR: The semigroup property for fractional integrals and fractional derivatives is established and properties of the kernel of q-fractional integral give rise to a q-analogue of Bernoulli polynomials, which are now polynomsials of two variables, x and y.

TL;DR: The influence of politics on the life of Soviet mathematicians in Stalin's era 1928–1953, years that witnessed the full unfolding of the dictator's power are described.

TL;DR: It is shown that @c"n(@a)/n->(j"("@a"-"1")"/"2"," "1)^-^1 as n->~, where j"@n," "1 is the first positive zero of the Bessel function J"@ n(z).

TL;DR: It is shown that CN contains universal measures, that is, probability measures for which the sequence {|?n|2d?}n?0 is dense in the set of all probability measures equipped with the weak-* topology.

TL;DR: Using strong subdifferentiability of convex functionals, it is shown that a finite codimensional subspace Y of K(l2) is strongly proximinal if and only if every linear form which vanishes on Y attains its norm.

TL;DR: The term appropriate means here the same as the authors need for a function f in order to have convergence for its Fourier series associated with the standard inner product given by the measure µ.

TL;DR: Estimating the degree of approximation of f by polynomials which are coconvex with it, namely, polynoms that change their convexity exactly at the points where f does is discussed.

TL;DR: The Askey-Wilson function transform is a q-analogue of the Jacobi function transform with kernel given by an explicit non-polynomial eigenfunction of the As key-Wilson second order q-difference operator.