Generalized Derivatives and Approximation by Polynomials

Generalized Derivatives and Approximation by Polynomials*

Approximation by Critical Points of Generalized Chebyshev Polynomials

We show that any compact, connected set in the plane can be approximated by the critical points of a polynomial with only two critical values. Date: April 2011. 1991 Mathematics Subject Classification. Primary: 30C62 Secondary:

The Degree of Approximation for Generalized Polynomials

The classical Mu'ntz theorem and the so-called Jackson-Muntz theorems concern uniform approximation on [0,1 ] by polynomials whose exponents are taken from an increasing sequence of positive real numbers A. Under mild restrictions on the exponents, the degree of approximation for A-poly nomials with real coefficients is compared with the corresponding degree of approximation when the coefficien...

Approximation by homogeneous polynomials

A new, elementary proof is given for the fact that on a centrally symmetric convex curve on the plane every continuous even function can be uniformly approximated by homogeneous polynomials. The theorem has been proven before by Benko and Kroó, and independently by Varjú using the theory of weighted potentials. In higher dimension the new method recaptures a theorem of Kroó and Szabados, which ...

Approximation by polynomials

1. Introduction 2. The Weierstrass approximation theorem 3. Estimates for the Bernstein polynomials 4. Weierstrass' original proof 5. The Stone–Weierstrass approximation theorem 6. Chebyshev's theorems 7. Approximation by polynomials and trigonometric polynomials 8. The nonexistence of a continuous linear projection 9. Approximation of functions of higher regularity 10. Inverse theorems Referen...