Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (1982), pp. 43-48
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A. K. Ramazanov. Rational functions of best approximation in integral metrics. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (1982), pp. 43-48. http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a11/
@article{VMUMM_1982_5_a11,
author = {A. K. Ramazanov},
title = {Rational functions of best approximation in integral metrics},
journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
pages = {43--48},
year = {1982},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a11/}
}
TY - JOUR
AU - A. K. Ramazanov
TI - Rational functions of best approximation in integral metrics
JO - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY - 1982
SP - 43
EP - 48
IS - 5
UR - http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a11/
LA - ru
ID - VMUMM_1982_5_a11
ER -
%0 Journal Article
%A A. K. Ramazanov
%T Rational functions of best approximation in integral metrics
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 1982
%P 43-48
%N 5
%U http://geodesic.mathdoc.fr/item/VMUMM_1982_5_a11/
%G ru
%F VMUMM_1982_5_a11
We prove that any rational function of degree $\le n$ with real coefficients best approximating a function $f\in L_q(a,b)$, $1, in the metric of $L_q(a,b)$ is of degree exactly $n$. We find the signs of the polynomials best approximating in the metric of $L_q([a,b])$, $1\le q\le\infty$ for some classes of differentiate functions.
