Numerical reconstruction of the first band(s) in an inverse Hill’s problem
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 59.

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).

DOI : 10.1051/cocv/2019031
Classification : 35P05, 58C40, 34K29, 34L15
Mots-clés : Inverse spectral theory, Hill’s operator, periodic Schrödinger operator, band structure, optimisation 
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     title = {Numerical reconstruction of the first band(s) in an inverse {Hill{\textquoteright}s} problem},
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Bakhta, Athmane; Ehrlacher, Virginie; Gontier, David. Numerical reconstruction of the first band(s) in an inverse Hill’s problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 59. doi : 10.1051/cocv/2019031. http://www.numdam.org/articles/10.1051/cocv/2019031/

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