Abstract
We answer a question of O. Christensen about affine systems in L 2(ℝ). Specifically, we show that if the dilation factor a > 1 is transcendental, then cancellations cannot occur between different scales, in the conditions for the affine system to form a frame. Such cancellations are known to occur when a is an integer.
Original language | English (US) |
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Pages (from-to) | 211-216 |
Number of pages | 6 |
Journal | Proceedings of the American Mathematical Society |
Volume | 135 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2007 |
Keywords
- Affine system
- Frame
- Transcendental
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics