E. V. Mishchenko, “On an Example of Using the Sobolev Quadrature Formulas in Wavelet Theory”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2008, Volume 8, Issue 4,Pages <nobr>49

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On an Example of Using the Sobolev Quadrature Formulas in Wavelet Theory

E. V. Mishchenko^ab

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^b Novosibirsk State University

Abstract: 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.

UDC: 517.518.34+36

Received: 17.04.2008