Geodesic
Rate of approximation of piecewise-analytic functions by rational fractions in the $L_p$-metrics, $0$
Sbornik. Mathematics, Tome 36 (1980) no. 2, pp. 203-212 
N. S. Vyacheslavov. Rate of approximation of piecewise-analytic functions by rational fractions in the $L_p$-metrics, $0
@article{SM_1980_36_2_a4,
     author = {N. S. Vyacheslavov},
     title = {Rate of approximation of piecewise-analytic functions by rational fractions in the $L_p$-metrics, $0<p\leqslant\infty$},
     journal = {Sbornik. Mathematics},
     pages = {203--212},
     year = {1980},
     volume = {36},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1980_36_2_a4/}
}
TY  - JOUR
AU  - N. S. Vyacheslavov
TI  - Rate of approximation of piecewise-analytic functions by rational fractions in the $L_p$-metrics, $0
JO  - Sbornik. Mathematics
PY  - 1980
SP  - 203
EP  - 212
VL  - 36
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1980_36_2_a4/
LA  - en
ID  - SM_1980_36_2_a4
ER  - 
%0 Journal Article
%A N. S. Vyacheslavov
%T Rate of approximation of piecewise-analytic functions by rational fractions in the $L_p$-metrics, $0
%J Sbornik. Mathematics
%D 1980
%P 203-212
%V 36
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1980_36_2_a4/
%G en
%F SM_1980_36_2_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper estimates are found for $L_pR_n(f)$ – the least deviation in the $L_p$-metric, $0, of a piecewise analytic function $f$ from the rational functions of degree at most $n$. It is shown that these estimates are sharp in a well-defined sense. Bibliography: 13 titles.

[1] D. J. Newman, “Rational approximation to $|x|$”, Michigan Math. J., 11:1 (1964), 11–14 | DOI | MR | Zbl

[2] A. A. Gonchar, “Otsenki rosta ratsionalnykh funktsii i nekotorye ikh prilozheniya”, Matem. sb., 72(114) (1967), 489–503 | Zbl

[3] A. P. Bulanov, “Asimptotika dlya naimenshikh uklonenii $|x|$ ot ratsionalnykh funktsii”, Matem. sb., 76(118) (1968), 288–303 | MR | Zbl

[4] N. S. Vyacheslavov, “O ravnomernom priblizhenii $|x|$ ratsionalnymi funktsiyami”, DAN SSSR, 220:3 (1975), 512–515 | Zbl

[5] N. S. Vyacheslavov, “O naimenshikh ukloneniyakh funktsii $\sign x$ i ee pervoobraznykh ot ratsionalnykh funktsii v metrikakh $L_p$, $0

\le\infty$”, Matem. sb., 103(145) (1977), 24–36 | Zbl

[6] P. Szüsz, P. Turan, “On the constructive theory of functions III”, Studia Sci. Math. Hung., 1 (1966), 315–322 | MR | Zbl

[7] P. Turan, “On the approximation of piecewise analytic functions by rational functions”, Sovremennye problemy teorii analiticheskikh funktsii, izd-vo “Nauka”, Moskva, 1966, 296–300 | MR

[8] J. Szabados, “On rational $L_p$-approximation”, Acta Math. Acad. Sci. Hung., 23:1–2 (1972), 197–202 | DOI | MR | Zbl

[9] H. Tamás, “A racionális és a spline approximáció közti kapcsolatról”, Mat. Lapok, 24:3–4 (1977), 381–385

[10] V. N. Rusak, “Pryamye metody v ratsionalnoi approksimatsii so svobodnymi polyusami”, Mezhdunarodnaya konferentsiya po konstruktivnoi teorii funktsii (Blagoevgrad, 30.V-4.VI.1977), Tezisy dokladov, 28 | Zbl

[11] G. M. Fikhtengolts, Kurs differentsialnogo i integralnogo ischisleniya, t. 1, Fizmatgiz, Moskva, 1962

[12] N. I. Akhiezer, Lektsii po teorii approksimatsii, izd-vo “Nauka”, Moskva, 1965 | MR

[13] S. B. Stechkin, Yu. N. Subbotin, Splainy v vychislitelnoi matematike, izd-vo “Nauka”, Moskva, 1976 | MR