On the orthorecursive expansion with respect to a~certain function system with computational errors in the~coefficients
Sbornik. Mathematics, Tome 195 (2004) no. 7, pp. 935-949
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Orthorecursive expansions with computational errors in the coefficients
are considered. An example of a system of functions on an interval of the real axis is presented such that the corresponding orthorecursive expansion
converges to the expanded element for arbitrary errors satisfying certain rather weak conditions. For various classes of expanded functions results on a.e. convergence, convergence in the $L^p$-metrics ($1\leqslant p\infty$), and uniform convergence are established.
@article{SM_2004_195_7_a1,
author = {V. V. Galatenko},
title = {On the orthorecursive expansion with respect to a~certain function system with computational errors in the~coefficients},
journal = {Sbornik. Mathematics},
pages = {935--949},
publisher = {mathdoc},
volume = {195},
number = {7},
year = {2004},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2004_195_7_a1/}
}
TY - JOUR AU - V. V. Galatenko TI - On the orthorecursive expansion with respect to a~certain function system with computational errors in the~coefficients JO - Sbornik. Mathematics PY - 2004 SP - 935 EP - 949 VL - 195 IS - 7 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SM_2004_195_7_a1/ LA - en ID - SM_2004_195_7_a1 ER -
%0 Journal Article %A V. V. Galatenko %T On the orthorecursive expansion with respect to a~certain function system with computational errors in the~coefficients %J Sbornik. Mathematics %D 2004 %P 935-949 %V 195 %N 7 %I mathdoc %U http://geodesic.mathdoc.fr/item/SM_2004_195_7_a1/ %G en %F SM_2004_195_7_a1
V. V. Galatenko. On the orthorecursive expansion with respect to a~certain function system with computational errors in the~coefficients. Sbornik. Mathematics, Tome 195 (2004) no. 7, pp. 935-949. http://geodesic.mathdoc.fr/item/SM_2004_195_7_a1/