Geodesic
On convergence of orthonormal expansions for exponential weights
Electronic transactions on numerical analysis, Tome 25 (2006), pp. 467-479.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let be a real interval, finite or infinite, and let . Assume that $\textcent $###$\sterling $########$\ddot $§$\copyright \copyright \textcent $### !####"$\\%' )( is a weight, so that we may define orthonormal polynomials corresponding to . For , let 0( 123\textcent 4 65 798A@ 1$B denote the th partial sum of the orthonormal expansion of with respect to these polynomials. We show that if C 1 , then as . The class of weights considered 1D#FEHGPI)$$###$$Q$\textcent $SR4G $$###$$T$\textcent $ UV$$###$$Q7 @ 1$BW{\S}X1W0U`Ybadcfe`gh i" Cp !\% 8 ( includes even exponential weights.$
Classification : 65N12, 65F35, 65J20, 65N55
Keywords: orthonormal polynomials, de la vall$\acute $ee poussin means 
@article{ETNA_2006__25__a2,
     author = {Mashele, H.P.},
     title = {On convergence of orthonormal expansions for exponential weights},
     journal = {Electronic transactions on numerical analysis},
     pages = {467--479},
     publisher = {mathdoc},
     volume = {25},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2006__25__a2/}
}
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Mashele, H.P. On convergence of orthonormal expansions for exponential weights. Electronic transactions on numerical analysis, Tome 25 (2006), pp. 467-479. http://geodesic.mathdoc.fr/item/ETNA_2006__25__a2/