A family of nonseparable scaling functions and compactly supported tight framelets

@article{Antoln2013AFO,
title={A family of nonseparable scaling functions and compactly supported tight framelets},
author={A. S. Antol{\'i}n and R. A. Zalik},
journal={Journal of Mathematical Analysis and Applications},
year={2013},
volume={404},
pages={201-211}
}

Abstract Given integers b and d , with d > 1 and | b | > 1 , we construct even nonseparable compactly supported refinable functions with dilation factor b that generate multiresolution analyses on L 2 ( R d ) . These refinable functions are nonseparable, in the sense that they cannot be expressed as the product of two functions defined on lower dimensions. We use these scaling functions and a slight generalization of a theorem of Lai and Stockler to construct smooth compactly supported tight… Expand