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Spectral asymptotics for Schrödinger operators with periodic point interactions. (English) Zbl 1006.34081
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.

34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
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