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Forster, B.* ; Massopust, P.

Splines of complex order: Fourier, filters and fractional derivatives.

Sampl. Theor. Signal Image Process. 10, 89-109 (2011)
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For the Schoenberg (polynomial) B-splines, interesting relations between their functional representation, Dirichlet averages, and difference operators are known. We use these relations to extend B-splines to an arbitrary (infinite) sequence of knots and to higher dimensions. The Fourierdomain representation of multidimensional complex B-splines, their twoscale relation and an explicit time domain representation are given for the case of equidistantly distributed knots on rays. In addition, we show that complex B-splines are solutions of the sampling/interpolation problem of complex order.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Complex B-splines; Dirichlet means, Scaling relation; Ridge functions; ultivariate splines; Fractional derivative and integral; Sampling series; Dirac comb; Mittag-Leffler function; Lizorkin space
ISSN (print) / ISBN 1530-6429
Quellenangaben Band: 10, Heft: 1-2, Seiten: 89-109 Artikelnummer: , Supplement: ,
Verlag Sampling Publishing
Begutachtungsstatus Peer reviewed