Approximation by transcendental polynomials
نویسندگان
چکیده
منابع مشابه
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 ...
متن کاملApproximation 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...
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These notes are prepared as lecture notes exclusively for the participants of this conference only. Any reproduction in any media, or any use for any other purpose of any part of this manuscript, without an expressed written consent of the author is unlawful.thorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conc...
متن کاملApproximation by Polynomials
1. Let In ;) be a set of distinct positive integers. According to a theorem of Müntz and Szász, the condition En-' .' =-is necessary and sufficient in order that polynomials in the powers x"' and 1 suffice to approximate uniformly an arbitrary continuous function in the interval 0 < x < 1, i .e ., that these powers span the space C of continuous functions in that interval. If the series converg...
متن کاملApproximation by weighted polynomials
It is proven that if xQ′(x) is increasing on (0,+∞) and w(x) = exp(−Q) is the corresponding weight on [0,+∞), then every continuous function that vanishes outside the support of the extremal measure associated with w can be uniformly approximated by weighted polynomials of the form wPn. This problem was raised by V. Totik, who proved a similar result (the Borwein-Saff conjecture) for convex Q. ...
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 1985
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap-46-1-299-309