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Lp estimates for joint quasimodes of semiclassical pseudodifferential operators

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Abstract

We develop a set of Lp estimates for functions u that are joint quasi-modes (approximate eigenfunctions) of r semiclassical pseudodifferential operators p1(x, hD),...,pr(x, hD). This work extends Sarnak [10] and Marshall’s [8] work on symmetric space to cover a more general class of manifolds/operators.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Otago Dunedin, Otago, 9016, New Zealand

    Melissa Tacy

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  1. Melissa Tacy
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Correspondence to Melissa Tacy.

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Tacy, M. Lp estimates for joint quasimodes of semiclassical pseudodifferential operators. Isr. J. Math. 232, 401–425 (2019). https://doi.org/10.1007/s11856-019-1878-2

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  • DOI: https://doi.org/10.1007/s11856-019-1878-2

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