Relations between the support of a compactly supported function and the exponential-polynomials spanned by its integer translates |
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Authors: | Amos Ron |
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Affiliation: | 1. Department of Mathematics, Texas A&M University, 77843, College Station, Texas, USA
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Abstract: | The interrelation between the shape of the support of a compactly supported function and the space of all exponential-polynomials spanned by its integer translates is examined. The results obtained are in terms of the behavior of these exponential-polynomials on certain finite subsets ofZs, which are determined by the support of the given function. Several applications are discussed. Among these is the construction of quasi-interpolants of minimal support and the construction of a piecewise-polynomial whose integer translates span a polynomial space which is not scale-invariant. As to polynomial box splines, it is proved here that in many cases a polynomial box spline admits a certain optimality condition concerning the space of the total degree polynomials spanned by its integer translates: This space is maximal compared with the spaces corresponding to other functions with the same supportCommunicated by Klaus Höllig. |
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Keywords: | KeywordHeading" > and phrases Multivariate splines Compactly supported functions Integer translates Piecewise-polynomials Polynomial box splines Exponential box splines Box splines |
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