Duke Mathematical Journal

L p eigenfunction bounds for the Hermite operator

Herbert Koch and Daniel Tataru

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We obtain L p eigenfunction bounds for the harmonic oscillator $H = -\Delta + x^2$ H = - Δ + x 2 in $\mathbb{R}^n$ n and for other related operators, improving earlier results of Thangavelu and of Karadzhov. We also construct suitable counterexamples that show that our estimates are sharp.

Article information

Duke Math. J., Volume 128, Number 2 (2005), 369-392.

First available in Project Euclid: 2 June 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35S05: Pseudodifferential operators
Secondary: 35B60: Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx]


Koch, Herbert; Tataru, Daniel. $L^p$ eigenfunction bounds for the Hermite operator. Duke Math. J. 128 (2005), no. 2, 369--392. doi:10.1215/S0012-7094-04-12825-8. https://projecteuclid.org/euclid.dmj/1117728419

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