A construction of biorthogonal functions to B-splines with multiple knots

We present a construction of a refinable compactly supported vector of func tions which is biorthogonal to the vector of B-splines of a given degree wi th multiple knots at the integers with prescribed multiplicity. The constru ction is based on Hermite interpolatory subdivision schemes, and on the rel ation between B-splines and divided differences. The biorthogonal vector of functions is shown to be refinable, with a mask related to that of the Her mits scheme. For simplicity of presentation the special (scalar) case, corr esponding to B-splines with simple knots, is treated separately. (C) 2000 A cademic Press.