caa a22 4500 605525544 CHVBK 20210128100759.0 cr unu---uuuuu 210128e20150701xx s 000 0 eng 10.1007/s10958-015-2435-0 doi (NATIONALLICENCE)springer-10.1007/s10958-015-2435-0 Komarov M. A. G. and N. G. Stoletov Vladimir State University, 87, Gor'kogo St., 600000, Vladimir, Russia aut An Analog of the Haar Condition for Simple Partial Fractions [Elektronische Daten] [M. Komarov] We prove that for a continuous real-valued function f on the segment [−1, 1] a real-valued simple partial fraction R n with n distinct poles outside the unit disk is a fraction of degree at most n of best approximation and is unique if and only if for the difference f − R n on [−1, 1] there exists a Chebyshev alternance of n + 1 points. The result is applied to the problem on approximation of real constants. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 208/2(2015-07-01), 174-180 1072-3374 208:2<174 2015 208 10958 https://doi.org/10.1007/s10958-015-2435-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2435-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Komarov M. A. G. and N. G. Stoletov Vladimir State University, 87, Gor'kogo St., 600000, Vladimir, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 208/2(2015-07-01), 174-180 1072-3374 208:2<174 2015 208 10958