Galkowski, J;
(2021)
Complete asymptotic expansions of the spectral function for symbolic perturbations of almost periodic Schrödinger operators in dimension one.
Journal of Spectral Theory
(In press).
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Abstract
In this article we consider asymptotics for the spectral function of Schr¨odinger operators on the real line. Let P : L 2 (R) → L 2 (R) have the form P := − d 2 dx2 + W, where W is a self-adjoint first order differential operator with certain modified almost periodic structure. We show that the kernel of the spectral projector, 1(−∞,λ2] (P) has a full asymptotic expansion in powers of λ. In particular, our class of potentials W is stable under perturbation by formally self-adjoint first order differential operators with smooth, compactly supported coefficients. Moreover, it includes certain potentials with dense pure point spectrum. The proof combines the gauge transform methods of Parnovski-Shterenberg and Sobolev with Melrose’s scattering calculus.
| Type: | Article |
|---|---|
| Title: | Complete asymptotic expansions of the spectral function for symbolic perturbations of almost periodic Schrödinger operators in dimension one |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://www.ems-ph.org/journals/journal.php?jrn=js... |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices 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/10118966 |
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