The convergence of least squares approximations for dual orthogonal series
Glasgow mathematical journal, Tome 15 (1974) no. 1, pp. 82-84
Voir la notice de l'article provenant de la source Cambridge University Press
The convergence of least squares approximations for dual orthogonal series in Hilbert space is established, thus providing a theorem applicable to practically all dual orthogonal series (such as dual trigonometric series, dual Bessel series, etc.) that have appeared in the literature. Our results establish for such dual series the existence of a sequence of functions satisfying in the L2norm the dual series relation, with an error tending to zero and, in particular, rigorously justify the calculations in [2] which showed least squares to be a practical approximation procedure for dual trigonometric equations. In fact, the desire to provide a rigorous convergence theorem for [2] motivated this study.
Feinerman, Robert P.; Kelman, Robert B. The convergence of least squares approximations for dual orthogonal series. Glasgow mathematical journal, Tome 15 (1974) no. 1, pp. 82-84. doi: 10.1017/S0017089500002184
@article{10_1017_S0017089500002184,
author = {Feinerman, Robert P. and Kelman, Robert B.},
title = {The convergence of least squares approximations for dual orthogonal series},
journal = {Glasgow mathematical journal},
pages = {82--84},
year = {1974},
volume = {15},
number = {1},
doi = {10.1017/S0017089500002184},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500002184/}
}
TY - JOUR AU - Feinerman, Robert P. AU - Kelman, Robert B. TI - The convergence of least squares approximations for dual orthogonal series JO - Glasgow mathematical journal PY - 1974 SP - 82 EP - 84 VL - 15 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500002184/ DO - 10.1017/S0017089500002184 ID - 10_1017_S0017089500002184 ER -
%0 Journal Article %A Feinerman, Robert P. %A Kelman, Robert B. %T The convergence of least squares approximations for dual orthogonal series %J Glasgow mathematical journal %D 1974 %P 82-84 %V 15 %N 1 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089500002184/ %R 10.1017/S0017089500002184 %F 10_1017_S0017089500002184
[1] 1.Achiezer, N. I. and Glasmann, I. M., Theorie der linearen Operatoren in Hilbert-Raum (Berlin, 1954). Google Scholar
[2] 2.Kelman, R. B. and Koper, C. A. Jr, Least squares approximations for dual trigonometric series, Glasgow Math. J. 14 (1973), 111–119. Google Scholar | DOI
[3] 3.Mikhlin, S. G. and Smolitskiy, K. L., Approximate methods for solution of differential and integral equations (New York, 1967). Google Scholar
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