Explicit Examples of Eigenfunctions of the Hermite Operator Saturating Some L p Bounds

Abstract

The goal of the paper is to provide a sequence of eigenfunctions that saturates the $L^{p}$ bounds obtained by Koch and Tataru for the multidimensional Hermite operator. More precisely, several such sequences of eigenfunctions have already been identified by Koch and Tataru, and we present an example in another range of $p$ .

Keywords

Hermite operator quantum harmonic oscillator eigenfunctions Lebesgue spaces

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