Uncertainty principle via variational calculus on modulation spaces
Journal article, Peer reviewed
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Date
2022Metadata
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- Institutt for matematiske fag [2359]
- Publikasjoner fra CRIStin - NTNU [37304]
Original version
doi.org/10.1016/j.jfa.2022.109605Abstract
We approach uncertainty principles of Cowling-Price-Heis-enberg-type as a variational principle on modulation spaces. In our discussion we are naturally led to compact localization operators with symbols in modulation spaces. The optimal constant in these uncertainty principles is the smallest eigenvalue of the inverse of a compact localization operator. The Euler-Lagrange equations for the associated functional provide equations for the eigenfunctions of the smallest eigenvalue of these compact localization operators. As a by-product of our proofs we derive a generalization to mixed-norm spaces of an inequality for Wigner and Ambiguity functions due do Lieb.