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Uncertainty principle via variational calculus on modulation spaces

2022; Elsevier BV; Volume: 283; Issue: 8 Linguagem: Inglês

10.1016/j.jfa.2022.109605

1096-0783

Nuno Costa Dias, Franz Luef, João Nuno Prata,

Seismic Imaging and Inversion Techniques

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.