Characterization of compactly supported refinable splines with integer matrix

Abstract

Let M be an integer matrix with absolute values of all its eigenvalues being greater than 1. We give a characterization of compactly supported M-refinable splines f and the conditions that the shifts of f form a Riesz basis.

Keywords:

• spline
• refinement
• blockwise polynomial
• Riesz basis
• simplex decomposition

AMS Subject Classifications:

• 42C40
• 39A70
• 41A15
• 41A30
• 65D07
• 65D18
• 65T60

Acknowledgements

We wish to thank the editor and referees for their helpful comments and suggestions. Yu-jing Guan was supported by the 985 project of Jilin University.