Bounds on eigenfunctions of semiclassical operators with double characteristics

Article type: Research Article

Authors: Krupchyk, Katya^a | Uhlmann, Gunther^{b; *}

Affiliations: [a] Department of Mathematics, University of California, Irvine, CA 92697-3875, USA. E-mail: katya.krupchyk@uci.edu | [b] Department of Mathematics, University of Washington, Seattle, WA 98195-4350, USA. E-mail: gunther@math.washington.edu

Correspondence: [*] Corresponding author. E-mail: gunther@math.washington.edu.

Abstract: We obtain sharp uniform bounds on the low lying eigenfunctions for a class of semiclassical pseudodifferential operators with double characteristics and complex valued symbols, under the assumption that the quadratic approximations along the double characteristics are elliptic.

Keywords: Semiclassical operators, double characteristics, low lying eigenfunctions

DOI: 10.3233/ASY-171442

Journal: Asymptotic Analysis, vol. 106, no. 1, pp. 25-46, 2018