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The rate of approximation by means of polynomials with restricted coefficients |
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| Authors: | J Bak M v Golitschek D Leviatan |
| Institution: | 1. City College of New York, New York, N.Y., USA 2. University of Würzburg, Würzburg Am Hubland, BRD 3. Tel Aviv University, Tel Aviv, Israel |
| Abstract: | For a sequenceA = {Ak} k?1 ∞ of positive constants letP A = {p(x): p(x) = Σ k?1 n a k x k ,n = 1,2, …, ¦a k ≦ A k k }. We consider the rate of approximation by elements ofP A , of continuous functions in 0, 1] which vanish at x = 0. Also a classP A is called “efficient” if globally it guarantees the Jackson rate of approximation. Some necessary conditions for efficiency and some sufficient ones are derived. |
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