Conjugate Functions on the Closed Interval and Their Relationship with Uniform Rational and Piecewise Polynomial Approximations

T. S. Mardvilko ; A. A. Pekarskii

Matematičeskie zametki, Tome 99 (2016) no. 2, pp. 248-261.

Résumé

Earlier the second author showed that, in the periodic case, the rate of best uniform rational approximations of a function is well described in terms of the rates of best uniform piecewise polynomial approximations of the function itself and its conjugate. In the present paper, a similar result is obtained for a closed interval.

Détail

Keywords: best uniform rational approximation of a function, best uniform piecewise polynomial approximation, $L_p$-modulus of smoothness, Jordan curve, Szegö-type inequality.
Mots-clés : Besov space $B_p^\alpha$

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