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

  • Aleksei Kulikov

    Norwegian University of Science and Technology, Trondheim, Norway
  • Lucas Oliveira

    Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil
  • João P. G. Ramos

    ETH Zürich, Switzerland
On Gaussian decay rates of harmonic oscillators and equivalences of related Fourier uncertainty principles cover
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Abstract

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.

Cite this article

Aleksei Kulikov, Lucas Oliveira, João P. G. Ramos, On Gaussian decay rates of harmonic oscillators and equivalences of related Fourier uncertainty principles. Rev. Mat. Iberoam. (2023), published online first

DOI 10.4171/RMI/1426