Abstract
In this paper we study some basic properties of multiresolution analysis of multiplicityd in several variables and discuss some examples related to the spaces of cardinal splines with respect to the unidiagonal or the crisscross partition of the plane. Furthermore, in analogy with [8], we show that if the scaling functions are compactly supported, then it is possible to find compactly supported mother waveletsψ l ,l=1,...,2n d−d, in such a way that the family {2jn/2 ψ l (2j x−v)} is a semiorthogonal basis ofL 2 (ℝn).
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De Michele, L., Soardi, P.M. On multiresolution analysis of multiplicityd . Monatshefte für Mathematik 124, 255–272 (1997). https://doi.org/10.1007/BF01298247
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DOI: https://doi.org/10.1007/BF01298247