Two-scale symbol and autocorrelation symbol for B-splines with multiple knots |
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Authors: | Gerlind Plonka |
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Institution: | (1) Fachbereich Mathematik, Universit?t Rostock, D-18051 Rostock, Germany |
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Abstract: | The Fourier transforms of B-splines with multiple integer knots are shown to satisfy a simple recursion relation. This recursion
formula is applied to derive a generalized two-scale relation for B-splines with multiple knots. Furthermore, the structure
of the corresponding autocorrelation symbol is investigated.
In particular, it can be observed that the solvability of the cardinal Hermite spline interpolation problem for spline functions
of degree 2m+1 and defectr, first considered by Lipow and Schoenberg 9], is equivalent to the Riesz basis property of our B-splines with degreem and defectr. In this way we obtain a new, simple proof for the assertion that the cardinal Hermite spline interpolation problem in 9]
has a unique solution. |
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Keywords: | B-splines with multiple knots two-saale symbol autocorrelation symbol Riesz basis cardinal hermite spline interpolation |
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