TY - JOUR
T1 - A Construction of Biorthogonal Functions to B-Splines with Multiple Knots
AU - Dyn, N.
PY - 2000/1
Y1 - 2000/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=14244261558&partnerID=8YFLogxK
U2 - 10.1006/acha.2000.0278
DO - 10.1006/acha.2000.0278
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AN - SCOPUS:14244261558
SN - 1063-5203
VL - 8
SP - 24
EP - 31
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
IS - 1
ER -