Complex B-splines
نویسندگان
چکیده
منابع مشابه
Complex B - splines
We propose a complex generalization of Schoenberg’s cardinal splines. To this end, we go back to the Fourier domain definition of the B-splines and extend it to complex-valued degrees. We show that the resulting complex B-splines are piecewise modulated polynomials, and that they retain most of the important properties of the classical ones: smoothness, recurrence, and two-scale relations, Ries...
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The notion of complex B-spline is extended to a multivariate setting by means of ridge functions employing the known geometric relationship between ordinary B-splines and multivariate B-splines. To derive properties of complex B-splines in R, 1 < s ∈ N, the Dirichlet average has to be generalized to include infinite dimensional simplices △∞. Based on this generalization several identities of mu...
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A relation between double Dirichlet averages and multivariate complex B-splines is presented. Based on this reationship, a formula for the computation of certain moments of multivariate complex B-splines is derived.
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A new type of B-spline the expo-rational B-spline is introduced. The heuristic motivation for its introduction comes from important similarities in several celebrated mathematical constructions originating in approximation theory, differential geometry and operator theory. The main result of the paper is the derivation of an Edgeworth and a steepest-descent/saddlepoint asymptotic expansion whic...
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For the Schoenberg B-splines, interesting relations between their functional representation, Dirichlet averages and difference operators are known. We use these relations to extend the B-splines to an arbitrary (infinite) sequence of knots and to higher dimensions. A new Fourier domain representation of the multidimensional complex B-spline is given. 1. Complex B-Splines Complex B-splines are a...
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ژورنال
عنوان ژورنال: Applied and Computational Harmonic Analysis
سال: 2006
ISSN: 1063-5203
DOI: 10.1016/j.acha.2005.07.003