UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

Complete asymptotic expansions of the spectral function for symbolic perturbations of almost periodic Schrödinger operators in dimension one

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). Green open access

[thumbnail of 2011.09245v1.pdf]
Preview
Text
2011.09245v1.pdf - Accepted Version

Download (336kB) | Preview

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.ucl.ac.uk/id/eprint/10118966
Downloads since deposit
10Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item