Journal Title
Title of Journal: J Fourier Anal Appl
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Abbravation: Journal of Fourier Analysis and Applications
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Authors: Jakob Lemvig Kamilla Haahr Nielsen
Publish Date: 2016/03/02
Volume: 22, Issue: 6, Pages: 1440-1451
Abstract
The frame set conjecture for Bsplines B n n ge 2 states that the frame set is the maximal set that avoids the known obstructions We show that any hyperbola of the form ab=r where r is a rational number smaller than one and a and b denote the sampling and modulation rates respectively has infinitely many pieces located around b=23dots not belonging to the frame set of the nth order Bspline This in turn disproves the frame set conjecture for Bsplines On the other hand we uncover a new region belonging to the frame set for Bsplines B n n ge 2The authors would like to thank Ole Christensen for posing the problem of characterizing the frame set of Bsplines in a talk at the Technical University of Denmark on February 3 2015 that initiated the work presented in this paper The authors would also like to thank Karlheinz Gröchenig and the referees for comments improving the presentation of the paper
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