On Gaussian decay rates of harmonic oscillators and equivalences of related Fourier uncertainty principles

• Aleksei Kulikov ^[1] ; Lucas Oliveira ^[2] ; João P. G. Ramos ^[3]
  1. [1] Norwegian University of Science and Technology

     Norwegian University of Science and Technology

     Noruega

     
  2. [2] Universidade Federal do Rio Grande do Sul

     Universidade Federal do Rio Grande do Sul

     Brasil

     
  3. [3] Swiss Federal Institute of Technology in Zurich

     Swiss Federal Institute of Technology in Zurich

     Zürich, Suiza

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 40, Nº 2, 2024, págs. 481-502
• Idioma: inglés
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  • We make progress on a question posed by Vemuri on the optimal Gaussian decay of harmonic oscillators, proving the original conjecture up to an arithmetic progression of times. The techniques used are a suitable translation of the problem at hand in terms of the free Schrödinger equation, the machinery developed in the work of Cowling, Escauriaza, Kenig, Ponce and Vega (2010), and a lemma which relates decay on average to pointwise decay.

    Such a lemma produces many more consequences in terms of equivalences of uncertainty principles. Complementing such results, we provide endpoint results in particular classes induced by certain Laplace transforms, both to the decay lemma and to the remaining cases of Vemuri’s conjecture, shedding light on the full endpoint question.