Galkowski, J;
Zworski, M;
(2022)
Viscosity Limits for Zeroth-Order Pseudodifferential Operators.
Communications on Pure and Applied Mathematics
, 75
(8)
pp. 1798-1869.
10.1002/cpa.22072.
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Abstract
Motivated by the work of Colin de Verdière and Saint-Raymond on spectral theory for zeroth-order pseudodifferential operators on tori, we consider viscosity limits in which zeroth-order operators, P, are replaced by P + iν Δ, ν > 0. By adapting the Helffer–Sjöstrand theory of scattering resonances, we show that, in a complex neighbourhood of the continuous spectrum, eigenvalues of P + iν Δ have limits as the viscosity ν goes to 0. In the simplified setting of tori, this justifies claims made in the physics literature. © 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.
| Type: | Article |
|---|---|
| Title: | Viscosity Limits for Zeroth-Order Pseudodifferential Operators |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1002/cpa.22072 |
| Publisher version: | https://doi.org/10.1002/cpa.22072 |
| Language: | English |
| Additional information: | © 2021 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10128037 |
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