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A compact set without Markov’s property but with an extension operator for C -functions

Alexander Goncharov (1996)

Studia Mathematica

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 L : ( K ) C [ 0 , 1 ] . 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

Szilárd Gy. Révész (2006)

Annales Polonici Mathematici

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 New Characterization of Weighted Peetre K-Functionals (II)

Draganov, Borislav, Ivanov, Kamen (2007)

Serdica Mathematical Journal

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

Rüdiger Verfürth (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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.

An Inequality for Trigonometric Polynomials

N. K. Govil, Mohammed A. Qazi, Qazi I. Rahman (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

The main result says in particular that if t ( ζ ) : = ν = - n c ν e i ν ζ 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.

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