IJPAM: Volume 13, No. 4 (2004)

PERIODIC SPLINE ORTHONORMAL BASES
CLOSEST TO PERIODIC $B$-SPLINES

Masaru Kamada$^1$, Rentsen Enkhbat$^2$
$^1$Department of Computer and Information Sciences
Ibaraki University
Hitachi, Ibaraki 316-8511, JAPAN
e-mail: kamada@cis.ibaraki.ac.jp
$^2$School of Mathematics and Computer Science
National University of Mongolia
P.O. Box 46/635, Ulaanbaatar, MONGOLIA
e-mail: renkhbat46@yahoo.com


Abstract.An orthonormal basis for the space of periodic cardinal splines is presented. This basis is closer to the $B$-spline basis than other orthonormal bases for the space, where the distance between two bases is measured as the total sum of $L^{2}$-metric between each basis function and its counterpart. Its convergence to a periodic version of cardinal function at the limit when the order tends to infinity is shown.

Received: April 6, 2004

AMS Subject Classification: 41A05, 41A15, 65D07, 65K10

Key Words and Phrases: periodic splines, orthonormal basis, $B$-splines

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 13
Issue: 4