Year: 2015
Type: preprint
Abstract: The frame set conjecture for B-splines $B_n$, $n \ge 2$, 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 $b=2,3,\dots$, \emph{not} belonging to the frame set of the $n$th order B-spline. This, in turn, disproves the frame set conjecture for B-splines. On the other hand, we uncover a new region belonging to the frame set for B-splines $B_n$, $n \ge 2$.
Source: arXiv (Cornell University)
Authors: Lemvig, Jakob, Nielsen, Kamilla Haahr
Institution: Technical University of Denmark
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Danmarks Tekniske Universitet
OpenAlex ID: W2953247686