Explicit Examples of Eigenfunctions of the Hermite Operator Saturating Some Lp Bounds

The goal of the paper is to provide a sequence of eigenfunctions that saturates the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:msup> <mml:mi>L</mml:mi> <mml:mi>p</mml:mi> </mml:msup> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>p</mml:mi> </mml:math> .