Journal article
Affine and quasi-affine frames for rational dilations
In this paper we extend the investigation of quasi-affine systems, which were originally introduced by Ron and Shen [J. Funct. Anal. 148 (1997), 408-447] for integer, expansive dilations, to the class of rational, expansive dilations. We show that an affine system is a frame if, and only if, the corresponding family of quasi-affine systems are frames with uniform frame bounds.
We also prove a similar equivalence result between pairs of dual affine frames and dual quasi-affine frames. Finally, we uncover some fundamental differences between the integer and rational settings by exhibiting an example of a quasi-affine frame such that its affine counterpart is not a frame.
Language: | English |
---|---|
Publisher: | American Mathematical Society |
Year: | 2011 |
Pages: | 1887-1924 |
ISSN: | 10886850 and 00029947 |
Types: | Journal article |
DOI: | 10.1090/S0002-9947-2010-05200-6 |
ORCIDs: | Lemvig, Jakob |