Functional Analysis and Its Applications

, Volume 47, Issue 2, pp 104–112

# Absence of eigenvalues for the periodic Schrödinger operator with singular potential in a rectangular cylinder

Article

## Abstract

We consider the periodic Schrödinger operator on a d-dimensional cylinder with rectangular section. The electric potential may contain a singular component of the form σ(x, y)δ Σ(x,y), where Σ is a periodic system of hypersurfaces. We establish that there are no eigenvalues in the spectrum of this operator, provided that Σ is sufficiently smooth and σL p,loc(Σ), p > d − 1.

## Key words

Schrödinger operator periodic coefficients absolutely continuous spectrum

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## Authors and Affiliations

1. 1.St. Petersburg Department of Steklov Mathematical InstituteSt. PetersburgRussia