<i>K</i>-Functional, Weighted Moduli of Smoothness, and Best Weighted Polynomial Approximation on a Simplex
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Acta Mathematica Sinica, English Series  1999, Vol. 15 Issue (3): 395-406    DOI: 10.1007/BF02650734
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K-Functional, Weighted Moduli of Smoothness, and Best Weighted Polynomial Approximation on a Simplex
Song Li
Department of Mathematics, Zhejiang University, 310027, Hangzhou, P.R.China
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Abstract An inverse theorem for the best weighted polynomial approximation of a function in (S) is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial approximation in , wherewα is a Jacobi-type weight on S, 0<p ≤ ∞,S is a simplex and Wλ is a Freud weight. For Ditzian-Totik K-functionals on Lp(S), 1 ≤p ≤ ∞, we obtain a new equivalence expression.
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Song Li
Key wordsWeighted moduli of smoothness   K-functional   Best weighted polynomial approximation   Simplex     
Received: 1998-03-06;
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Song Li. K-Functional, Weighted Moduli of Smoothness, and Best Weighted Polynomial Approximation on a Simplex[J]. Acta Mathematica Sinica, English Series, 1999, 15(3): 395-406.
http://www.actamath.com/Jwk_sxxb_en//EN/10.1007/BF02650734      or     http://www.actamath.com/Jwk_sxxb_en//EN/Y1999/V15/I3/395
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