Monatshefte für Mathematik

, Volume 124, Issue 3, pp 255–272 | Cite as

On multiresolution analysis of multiplicityd

  • L. De Michele
  • P. M. Soardi
Article

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 waveletsψl,l=1,...,2ndd, in such a way that the family {2jn/2ψl(2jxv)} is a semiorthogonal basis ofL2 (ℝn).

1991 Mathematics Subject Classification

42C15 

Key words

Multiresolution analysis multiplicityd compactly supported semi-orthogonal wavelets multivariate splines 

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • L. De Michele
    • 1
  • P. M. Soardi
    • 1
  1. 1.Dipartimento di MatematicaUniversità di MilanoMilanoItaly

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