-regularly varying functions in approximation theory.
A compact set without Markov’s property but with an extension operator for -functions
We give an example of a compact set K ⊂ [0, 1] such that the space ℇ(K) of Whitney functions is isomorphic to the space s of rapidly decreasing sequences, and hence there exists a linear continuous extension operator . At the same time, Markov’s inequality is not satisfied for certain polynomials on K.
A comparative analysis of Bernstein type estimates for the derivative of multivariate polynomials
We compare the yields of two methods to obtain Bernstein type pointwise estimates for the derivative of a multivariate polynomial in a domain where the polynomial is assumed to have sup norm at most 1. One method, due to Sarantopoulos, relies on inscribing ellipses in a convex domain K. The other, pluripotential-theoretic approach, mainly due to Baran, works for even more general sets, and uses the pluricomplex Green function (the Zaharjuta-Siciak extremal function). When the inscribed ellipse method...
A lower bound for the second moment of Schoenberg operator.
A Markov Type Inequality for Higher Derivates of Polynomials.
A modulus of smoothness based on an algebraic addition.
A New Characterization of Weighted Peetre K-Functionals (II)
2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10. ∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”, Sofia, 2006.Certain types of weighted Peetre K-functionals are characterized by means of the classical moduli of smoothness taken on a proper linear transforms of the function. The weights with power-type asymptotic at the ends of the interval with arbitrary real exponents are considered. This paper extends the method and results presented...
A note on polynomial approximation in Sobolev spaces
A note on polynomial approximation in Sobolev spaces
For domains which are star-shaped w.r.t. at least one point, we give new bounds on the constants in Jackson-inequalities in Sobolev spaces. For convex domains, these bounds do not depend on the eccentricity. For non-convex domains with a re-entrant corner, the bounds are uniform w.r.t. the exterior angle. The main tool is a new projection operator onto the space of polynomials.
A note on the sharpness of the Remez-type inequality for homogeneous polynomials on the sphere.
A pointwise approximation theorem for linear combinations of Bernstein polynomials.
A sharp Bernstein-type inequality for exponential sums.
A simple proof of the Chui-Smith theorem on Landau's problem
A survey of weighted polynomial approximation with exponential weights.
A weighted inequality for derivatives on the half-line.
About an estimation problem of Zahorski
About an old problem of Karamata.
An analogue of a problem of J. Balázs and P. Turán, II (Inequalities)
An inequality for polynomials with elliptic majorant.
An Inequality for Trigonometric Polynomials
The main result says in particular that if is a trigonometric polynomial of degree n having all its zeros in the open upper half-plane such that |t(ξ)| ≥ μ on the real axis and cₙ ≠ 0, then |t’(ξ)| ≥ μn for all real ξ.