Multivariate discrete splines and linear Diophantine equations
Author:
Rong Qing Jia
Journal:
Trans. Amer. Math. Soc. 340 (1993), 179-198
MSC:
Primary 41A15; Secondary 11D04, 39A10, 39A70, 41A63
DOI:
https://doi.org/10.1090/S0002-9947-1993-1159194-6
MathSciNet review:
1159194
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Abstract | References | Similar Articles | Additional Information
Abstract: In this paper we investigate the algebraic properties of multivariate discrete splines. It turns out that multivariate discrete splines are closely related to linear diophantine equations. In particular, we use a solvability condition for a system of linear diophantine equations to obtain a necessary and sufficient condition for the integer translates of a discrete box spline to be linearly independent. In order to understand the local structure of discrete splines we develop a general theory for certain systems of linear partial difference equations. Using this theory we prove that the integer translates of a discrete box spline are locally linearly independent if and only if they are linearly independent.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1993-1159194-6
Keywords:
Multivariate discrete splines,
linear diophantine equations,
linear independence,
translates,
partial difference equations
Article copyright:
© Copyright 1993
American Mathematical Society