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Uncertainty principle via variational calculus on modulation spaces.
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Autores
Orientador(es)
Resumo(s)
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.
Descrição
Palavras-chave
Cowling-Price uncertainty principle Variational problem Optimal constant Modulation spaces
Contexto Educativo
Citação
Dias, N. C., Luef, F., & Prata, J. N. (2022). Uncertainty principle via variational calculus on modulation spaces. Journal of Functional Analysis, 283(8), 109605.
Editora
Elsevier