On Laguerre expansions summability by the linear methods
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 1, pp. 15-20
Cet article a éte moissonné depuis la source Math-Net.Ru
This paper studies a problem of Laguerre expansions summability via methods defined by triangular matrices. The conditions on a matrix and an expandable function are obtained to guarantee the convergence of corresponding linear means at the Lebesgue point $t=0$.
@article{ISU_2008_8_1_a2,
author = {M. D. Burmistrova},
title = {On {Laguerre} expansions summability by the linear methods},
journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
pages = {15--20},
year = {2008},
volume = {8},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ISU_2008_8_1_a2/}
}
M. D. Burmistrova. On Laguerre expansions summability by the linear methods. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 8 (2008) no. 1, pp. 15-20. http://geodesic.mathdoc.fr/item/ISU_2008_8_1_a2/
[1] Sege G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962
[2] Faddeev D. K., “O predstavlenii summiruemykh funktsii singulyarnymi integralami v tochkakh Lebesgue'a”, Matem. cb., 1(43):3 (1936), 351–368 | Zbl
[3] Zigmund A., Trigonometricheskie ryady, v. I, Mir, M., 1965 | MR
[4] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1981 | MR
[5] Askey R., Wainger S., “Mean convergence of expansions in Laguerre and Hermite series”, Amer. J. Math., 87 (1965), 695–708 | DOI | MR | Zbl