Opuscula Mathematica
Opuscula Math. 36, no. 6 (), 807-818
http://dx.doi.org/10.7494/OpMath.2016.36.6.807
Opuscula Mathematica

On the spectrum of periodic perturbations of certain unbounded Jacobi operators


Abstract. It is known that a purely off-diagonal Jacobi operator with coefficients \(a_n=n^{\alpha}\), \(\alpha\in(0,1]\), has a purely absolutely continuous spectrum filling the whole real axis. We show that a 2-periodic perturbation of these operators creates a non trivial gap in the spectrum.
Keywords: essential spectrum, spectral gap, periodic perturbation.
Mathematics Subject Classification: 47A10, 47B36, 39A70.
Cite this article as:
Jaouad Sahbani, On the spectrum of periodic perturbations of certain unbounded Jacobi operators, Opuscula Math. 36, no. 6 (2016), 807-818, http://dx.doi.org/10.7494/OpMath.2016.36.6.807
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI http://dx.doi.org/10.7494/OpMath
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