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Some Qualitative Properties of Bivariate Euler-Frobenius Polynomials.

Author: C De Boor; K Hoellig; S Riemenschneider; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER.
Publisher: Ft. Belvoir Defense Technical Information Center OCT 1984.
Edition/Format:   Print book : English
Database:WorldCat
Summary:
This is a further report in a series devoted to the study of box splines. Box splines provide a natural generalization of univariate cardinal splines, i.e., splines with a uniform knot sequence. The process of univariate spline interpolation becomes particularly simple in the cardinal case, and this report considers the corresponding bivariate process of interpolation at the integer points in the plane to a given  Read more...
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Document Type: Book
All Authors / Contributors: C De Boor; K Hoellig; S Riemenschneider; WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER.
OCLC Number: 227633587
Description: 20 pages

Abstract:

This is a further report in a series devoted to the study of box splines. Box splines provide a natural generalization of univariate cardinal splines, i.e., splines with a uniform knot sequence. The process of univariate spline interpolation becomes particularly simple in the cardinal case, and this report considers the corresponding bivariate process of interpolation at the integer points in the plane to a given function by a linear combination of integer translates of a box spline. In particular, the report shows that this process is well posed, i.e., any bounded continuous function has exactly one such bounded interpolant If. The argument uses the Fourier transform to identify a certain trigonometric polynomial (in two variables) whose nonvanishing is equivalent to the asserted well-posedness. The minimum value of this polynomial yields a bound on the norm of the resulting interpolation projector I.

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