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A Construction of Biorthogonal Functions to B-Splines with Multiple Knots

✍ Scribed by N. Dyn

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 71 KB
Volume: 8
Category: Article
ISSN: 1063-5203
DOI: 10.1006/acha.2000.0278

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✦ Synopsis

We present a construction of a refinable compactly supported vector of functions which is biorthogonal to the vector of B-splines of a given degree with multiple knots at the integers with prescribed multiplicity. The construction is based on Hermite interpolatory subdivision schemes, and on the relation between B-splines and divided differences. The biorthogonal vector of functions is shown to be refinable, with a mask related to that of the Hermite scheme. For simplicity of presentation the special (scalar) case, corresponding to B-splines with simple knots, is treated separately.

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