Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 4, pp. 49-59
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E. V. Mishchenko. On an Example of Using the Sobolev Quadrature Formulas in Wavelet Theory. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 4, pp. 49-59. http://geodesic.mathdoc.fr/item/VNGU_2008_8_4_a5/
@article{VNGU_2008_8_4_a5,
author = {E. V. Mishchenko},
title = {On an {Example} of {Using} the {Sobolev} {Quadrature} {Formulas} in {Wavelet} {Theory}},
journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
pages = {49--59},
year = {2008},
volume = {8},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VNGU_2008_8_4_a5/}
}
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It is shown that Zhamalov’s polynomials give rise to Battle–Lemarie wavelets of arbitrary order; moreover, the Franklin system is not the Battle–Lemarie wavelet of order 1. Symmetry of the scaling functions and wavelets of arbitrary order in the Battle–Lemarie construction is proven.
[1] Bochkarëv S. V., Metod usrednenii v teorii ortogonalnykh ryadov i nekotorye voprosy teorii bazisov, Trudy Matematicheskogo instituta im. V. A. Steklova, CXLVI, Nauka, M., 1978 | MR | Zbl
[2] Dobeshi I., 10 lektsii po veivletam, RKhD, M.–Izhevsk, 2001
