| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 59 | |
| Number of page(s) | 18 | |
| DOI | https://doi.org/10.1051/cocv/2019031 | |
| Published online | 08 September 2020 | |
Numerical reconstruction of the first band(s) in an inverse Hill’s problem
1
Ecole des Ponts ParisTech,
Champs-sur-Marne, France.
2
Ecole des Ponts ParisTech & INRIA,
Champs-sur-Marne, France.
3
CEREMADE, Paris-Dauphine University, PSL University,
75016
Paris, France.
* Corresponding author: virginie.ehrlacher@enpc.fr
Received:
10
May
2018
Accepted:
26
April
2019
This paper concerns an inverse band structure problem for one dimensional periodic Schrödinger operators (Hill’s operators). Our goal is to find a potential for the Hill’s operator in order to reproduce as best as possible some given target bands, which may not be realisable. We recast the problem as an optimisation problem, and prove that this problem is well-posed when considering singular potentials (Borel measures).
Mathematics Subject Classification: 35P05 / 58C40 / 34K29 / 34L15
Key words: Inverse spectral theory / Hill’s operator / periodic Schrödinger operator / band structure / optimisation
© EDP Sciences, SMAI 2020
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.