In this paper we study some basic properties of multiresolution analysis of multiplicity d 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 wavelets psi(1), l = 1,..., 2(n) d - d, in such a way that the family {2(jn/2)psi(1)(2(j) x - v)} is a semi-orthogonal basis of L-2 (R-n)
DE MICHELE, L., Soardi, P. (1997). On multiresolution analysis of multiplicity d. MONATSHEFTE FÜR MATHEMATIK, 124(3), 255-272 [10.1007/BF01298247].
On multiresolution analysis of multiplicity d
DE MICHELE, LEONEDE;SOARDI, PAOLO MAURIZIO
1997
Abstract
In this paper we study some basic properties of multiresolution analysis of multiplicity d 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 wavelets psi(1), l = 1,..., 2(n) d - d, in such a way that the family {2(jn/2)psi(1)(2(j) x - v)} is a semi-orthogonal basis of L-2 (R-n)
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