Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On affine frames with transcendental dilations

Author: R. S. Laugesen
Journal: Proc. Amer. Math. Soc. 135 (2007), 211-216
MSC (2000): Primary 42C40; Secondary 42C15
Published electronically: June 29, 2006
MathSciNet review: 2280189
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We answer a question of O. Christensen about affine systems in $ L^2(\mathbb{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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42C40, 42C15

Retrieve articles in all journals with MSC (2000): 42C40, 42C15

Additional Information

R. S. Laugesen
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801

Keywords: Affine system, frame, transcendental
Received by editor(s): June 30, 2005
Received by editor(s) in revised form: July 31, 2005
Published electronically: June 29, 2006
Additional Notes: This work was completed during a Visiting Erskine Fellowship at the University of Canterbury, New Zealand, and also with support from National Science Foundation award DMS–0140481.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.