On the fundamental polynomials for Hermite-Fejér interpolation of Lagrange type on the Chebyshev nodes.
On the gamma and beta approximation operators.
On the iteration of . (Sur l'itéré de .)
On the lattice of polynomials with integer coefficients: the covering radius in
The paper deals with the approximation by polynomials with integer coefficients in , 1 ≤ p ≤ ∞. Let be the space of polynomials of degree ≤ n which are divisible by the polynomial , r ≥ 0, and let be the set of polynomials with integer coefficients. Let be the maximal distance of elements of from in . We give rather precise quantitative estimates of for n ≳ 6r. Then we obtain similar, somewhat less precise, estimates of for p ≠ 2. It follows that as n → ∞. The results partially...
On the maximum modulus of a polynomial and its derivatives.
On the maximum modulus of polynomials. II.
On the multivariate transfinite diameter
We prove several new results on the multivariate transfinite diameter and its connection with pluripotential theory: a formula for the transfinite diameter of a general product set, a comparison theorem and a new expression involving Robin's functions. We also study the transfinite diameter of the pre-image under certain proper polynomial mappings.
On the operator of Bleimann, Butzer and Hahn.
On the projection norm for a weighted interpolation using Chebyshev polynomials of the second kind.
On the rate of convergence of Hermite-Fejér polynomials to functions of bounded variation on the zeros of certain Jacobi polynomials
On the sharpness of an approximation criterion of smoothness for functions on a segment
On the strong summability and approximation of Fourier series
On the theorem of Géza Grünwald and Józef Marcinkiewicz
This survey is a tribute to Géza Grünwald and Józef Marcinkiewicz dealing with the so called Grünwald-Marcinkiewicz Theorem.
On weighted -approximation by polynomials
On Zeros of Polynomials of Best Approximation to Holomorphic and C... Functions.
Optimal Extrapolation of Derivatives.
Optimal Interval Refinement near Singularities.
Optimal Nodes for Interpolation in Hardy Spaces.
Optimal-order quadratic interpolation in vertices of unstructured triangulations
We study the problem of Lagrange interpolation of functions of two variables by quadratic polynomials under the condition that nodes of interpolation are vertices of a triangulation. For an extensive class of triangulations we prove that every inner vertex belongs to a local six-tuple of vertices which, used as nodes of interpolation, have the following property: For every smooth function there exists a unique quadratic Lagrange interpolation polynomial and the related local interpolation error...
Orthogonal Algebraic Polynomial Schauder Bases of Optimal Degree.