Abstract
The aim of this paper is to prove new uncertainty principles for the Weinstein operator. The first of these results is a sharp Heisenberg-type inequality for the Weinstein transform, that is, for and
,
The second result states that the previous inequality can be refined for an orthonormal basis for
, that is, if
is an orthonormal basis for
, then
As a side result, we prove a new version of Heisenberg's uncertainty inequality for the Weinstein–Gabor transform, which states that the Weinstein–Gabor transform of a nonzero function with respect to a nonzero window function cannot be time and frequency concentrated around zero.
Acknowledgments
The authors thank the anonymous referee for his/her careful reading of the manuscript that leads to a refinement presentation.
Disclosure statement
No potential conflict of interest was reported by the author(s).