Mathematical Research Letters

Volume 20 (2013)

Number 2

Pointwise bounds on quasimodes of semiclassical Schrödinger operators in dimension two

Pages: 401 – 408

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n2.a15

Authors

Hart F. Smith (Department of Mathematics, University of Washington, Seattle, Wash., U.S.A.)

Maciej Zworski (Department of Mathematics, University of California at Berkeley)

Abstract

We prove sharp pointwise bounds on quasimodes of semiclassical Schrödinger operators with arbitrary smooth real potentials in dimension two. This end-point estimate was left open in the general study of semiclassical $L^p$ bounds conducted by Koch et al. [2]. However, we show that the results of [2] imply the two-dimensional end-point estimate by scaling and localization.

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