Duke Mathematical Journal

L p eigenfunction bounds for the Hermite operator

Herbert Koch and Daniel Tataru

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Abstract

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

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

Dates
First available in Project Euclid: 2 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1117728419

Digital Object Identifier
doi:10.1215/S0012-7094-04-12825-8

Mathematical Reviews number (MathSciNet)
MR2140267

Zentralblatt MATH identifier
1075.35020

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

Citation

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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