On one question of Ed Saff.
On polynomials of least deviation from zero in several variables.
On Projection Constants of Polynomial Spaces on the Unit Ball in Several Variables.
On Representations of Algebraic Polynomials by Superpositions of Plane Waves
* The author was supported by NSF Grant No. DMS 9706883.Let P be a bi-variate algebraic polynomial of degree n with the real senior part, and Y = {yj }1,n an n-element collection of pairwise noncolinear unit vectors on the real plane. It is proved that there exists a rigid rotation Y^φ of Y by an angle φ = φ(P, Y ) ∈ [0, π/n] such that P equals the sum of n plane wave polynomials, that propagate in the directions ∈ Y^φ .
On restricted derivative approximation
On some constants in approximation by Bernstein operators.
On the approximation of analytic functions by the -Bernstein polynomials in the case .
On the approximation properties of Bernstein polynomials via probabilistic tools.
On the Bernstein-Walsh-Siciak theorem
By the Oka-Weil theorem, each holomorphic function f in a neighbourhood of a compact polynomially convex set can be approximated uniformly on K by complex polynomials. The famous Bernstein-Walsh-Siciak theorem specifies the Oka-Weil result: it states that the distance (in the supremum norm on K) of f to the space of complex polynomials of degree at most n tends to zero not slower than the sequence M(f)ρ(f)ⁿ for some M(f) > 0 and ρ(f) ∈ (0,1). The aim of this note is to deduce the uniform version,...
On the completeness of the system in
Let be the union of infinitely many disjoint closed intervals where , , , Let be a nonnegative function and a sequence of distinct complex numbers. In this paper, a theorem on the completeness of the system in is obtained where is the weighted Banach space consists of complex functions continuous on with vanishing at infinity.
On the convergence of generalized polynomial chaos expansions
A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial chaos expansions to the correct limit and complement...
On the convergence of generalized polynomial chaos expansions
A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial...
On the convergence properties of basic series representing Clifford valued functions.
On the Degre of L1-aproximation by Modified Bernstein Polynomials
On the degree of approximation by Bernstein operators.
On the degree of simultaneous approximation by modified Bernstein polynomials
On the denseness of Jacobi polynomials.
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 .)