Galkowski, Jeffrey Eric;
Parnovski, Leonid;
Stherenberg, Roman;
(2023)
Classical wave methods and modern gauge transforms: spectral asymptotics in the one dimensional case.
Geometric and Functional Analysis
, 33
pp. 1454-1538.
10.1007/s00039-023-00650-x.
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Abstract
In this article, we consider the asymptotic behaviour of the spectral function of Schrödinger operators on the real line. Let H:L²(R)→L²(R) have the form H:=-d²/dx²+Q, where Q is a formally self-adjoint first order differential operator with smooth coefficients, bounded with all derivatives. We show that the kernel of the spectral projector, 1₍₋∞,ₚ₂](H), has a complete asymptotic expansion in powers of ρ. This settles the 1-dimensional case of a conjecture made by the last two authors.
| Type: | Article |
|---|---|
| Title: | Classical wave methods and modern gauge transforms: spectral asymptotics in the one dimensional case |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00039-023-00650-x |
| Publisher version: | https://doi.org/10.1007/s00039-023-00650-x |
| Language: | English |
| Additional information: | © The Author(s), 2023. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. https://creativecommons.org/licenses/by/4.0/ |
| 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-pp.ucl.ac.uk/id/eprint/10174616 |
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