ABSTRACT
The subject of this paper is a natural generalization of the concept of inter p o la tor spline wavelets introduced in [2, p. 177]. Let {V™} (j E ZZ) be the multiresolution analysis of Z^IR) generated by the cardinal B-spline Nm of degree m. Further, with {W™ } (j E ZZ) we denote the sequence of wavelet spaces, in the sense that
where 0 indicates the orthogonal summation. Let T := {z E C, \z\ = 1}. With the help of the Euler-Frobenius
polynomial of degree 2m + 1
we introduce the cardinal fundamental spline L2m+i of degree 2m + 1
satisfying
with the Kronecker symbol δ. For m G IN the interpolatory wavelet ψιίΤη 1S defined by
where D denotes the differential operator. Then ψιίΤη generates the wavelet spaces W™ (j G 7L)
(cf. [2], p. 178).
