On Lagrange and Hermite Interpolation in Rk.
On multivariate approximation by Meyer-König-Zeller type polynomials.
On multivariate interpolation by weights.
On Müntz rational approximation in multivariables
The present paper shows that for any sequences of real numbers, each with infinitely many distinct elements, , j=1,...,s, the rational combinations of are always dense in .
On norms of factors of multivariate polynomials on convex bodies.
On Optimal Extreme-Discrepancy Point Sets in the Square.
On optimal triangular meshes for minimizing the gradient error.
On polynomials of least deviation from zero in several variables.
On Projection Constants of Polynomial Spaces on the Unit Ball in Several Variables.
On some generalization of box splines
We give a generalization of box splines. We prove some of their properties and we give applications to interpolation and approximation of functions.
On the approximation by compositions of fixed multivariate functions with univariate functions
The approximation in the uniform norm of a continuous function f(x) = f(x₁,...,xₙ) by continuous sums g₁(h₁(x)) + g₂(h₂(x)), where the functions h₁ and h₂ are fixed, is considered. A Chebyshev type criterion for best approximation is established in terms of paths with respect to the functions h₁ and h₂.
On the Construction of Multi-Dimensional Embedded Cubature Formulae.
On the control net of certain multivariate spline functions
On the least squares fit by radial functions to multidimensional scattered data.
On the local linear independence of translates of a box spline
On the order of approximation of functions by the bidimensional operators Favard-Szász-Mirakyan.
On the Uniform Norm of an Arbitrary Coefficient Functional over Finite Dimensional Subspaces of C (D).
Optimal Addition of Knots to Cubature Formulae for Planar Regions.
Optimal Cycles in Doubly Weighted Graphs and Approximation of Bivariate Functions by Univariate Ones.
Optimality of the range for which equivalence between certain measures of smoothness holds
Recently it was proved for 1 < p < ∞ that , a modulus of smoothness on the unit sphere, and , a K-functional involving the Laplace-Beltrami operator, are equivalent. It will be shown that the range 1 < p < ∞ is optimal; that is, the equivalence does not hold either for p = ∞ or for p = 1.