Regularity of the Schrödinger equation for the harmonic oscillator

Bruno Bongioanni Instituto de Matemática Aplicada del Litoral, CONICET Keith M. Rogers Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas

Analysis of PDEs mathscidoc:1701.03019

Arkiv for Matematik, 49, (2), 217-238, 2009.8
We consider the Schrödinger equation for the harmonic oscillator$i$$∂$_{$t$}$u$=$Hu$, where$H$=−Δ+|$x$|^{2}, with initial data in the Hermite–Sobolev space$H$^{−$s$/2}$L$^{2}(ℝ^{$n$}). We obtain smoothing and maximal estimates and apply these to perturbations of the equation and almost everywhere convergence problems.
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  title={Regularity of the Schrödinger equation for the harmonic oscillator},
  author={Bruno Bongioanni, and Keith M. Rogers},
  booktitle={Arkiv for Matematik},
Bruno Bongioanni, and Keith M. Rogers. Regularity of the Schrödinger equation for the harmonic oscillator. 2009. Vol. 49. In Arkiv for Matematik. pp.217-238.
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