Spectral asymptotics for Schrödinger operators with periodic point interactions (Q1604460)

Spectral asymptotics are considered for Schrödinger operators with periodic point interactions generated in \(L_2(\mathbb{R})\) by the expression \[ H=-{d^2\over dx^2}+\sum\limits_{n\in \mathbb{Z}}\alpha_n \delta(x-n), \] where \(\delta\) is the Dirac delta-function and \(\alpha_n\) are real constants. It is shown that the first terms in the asymptotics determine the class of unitary equivalent operators uniquely.