Abstract
We prove an express theorem on the stability of integer translates of a box spline and clear proposition 4. 10. 2 in [6] for box spline case. Also, we provide a way to construct a linear projection from Lp to the space of integer translates of a box spline. Consequently, the equivalence among the stability, global linear independence and local linear independence of translates of a box spile follows.
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References
de Boor, C. The Polynomials in the Linear Span of Integer Translates of a Compactly Supported Function, Constructive Approx., 3(1987), 199–208.
de Boor, C. & DeVore, R., Approximation by Smooth Multivariate Splines, Trans. Amer. Math. Soc., 276 (1983), 775–788.
de Boor, C. & Höllig, K., B-Spines from Parallelepipeds, J. Analyses Math., 62 (1982/83), 99–115.
Chui, C. K., Multivariate Splines: Theory and Applications, CBMS Vol 54, SIAM Publication, Philadelphia, 1988.
Dahmen, W. & Micchelli, C. A., On the Local Linear Independence of Translates of a Box Spline, Studia Math., 82 (1985), 243–262.
—, Recent Progress in Multivariate Splines, in Multivariate Approximation IV, C. K. Chui, L. L. Schumaker and J. Ward, Academic Press, New York 1983, 27–121.
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Partially supported by ARO contract No. DAAL 4-87-0025
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Mingjun, L. A remark on translates of a box spline. Approx. Theory & its Appl. 5, 97–104 (1989). https://doi.org/10.1007/BF02836119
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DOI: https://doi.org/10.1007/BF02836119