## Abstract The solvability of multivariate refinement equations in the Hilbert space __L__~2~(ℝ^__s__^) is studied. It is shown that the set of all __L__~2~‐solutions of such equations either consists of the trivial solution only or it contains a subspace isomorphic to a space __L__~∞~(__S__~__M__
✦ LIBER ✦
Multivariate nonhomogeneous refinement equations
✍ Scribed by Thomas B. Dinsenbacher; Douglas P. Hardin
- Publisher
- SP Birkhäuser Verlag Boston
- Year
- 1999
- Tongue
- English
- Weight
- 433 KB
- Volume
- 5
- Category
- Article
- ISSN
- 1069-5869
No coin nor oath required. For personal study only.
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In this paper we present an algorithm for the construction of uniformly continuous, compactly supported refinable interpolating functions for arbitrary dilation matrices. We investigate the asymptotic behavior of their symbols and we develop a link to the theory of translation invariant MRA.