T. S. Mardvilko, A. A. Pekarskii, “Conjugate Functions on the Closed Interval and Their Relationship with Uniform Rational and Piecewise Polynomial Approximations”, Mat. Zametki, 2016, Volume 99, Issue 2,Pages <nobr>248

This article is cited in 3 papers

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

T. S. Mardvilko^a, A. A. Pekarskii^b

^a Belarussian State University of Computer Science and Radioelectronic Engineering
^b Belarusian State University, Minsk

Abstract: 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.

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

UDC: 517.51+517.53

Received: 10.02.2015
Revised: 30.06.2015

DOI: 10.4213/mzm10672