Opuscula Math. 35, no. 3 (2015), 353-370
http://dx.doi.org/10.7494/OpMath.2015.35.3.353

Opuscula Mathematica

# Spectra of some selfadjoint Jacobi operators in the double root case

Wojciech Motyka

Abstract. In this paper we prove a mixed spectrum of Jacobi operators defined by $$\lambda_n=s(n)(1+x(n))$$ and $$q_n=-2s(n)(1+y(n))$$, where $$(s(n))$$ is a real unbounded sequence, $$(x(n))$$ and $$(y(n))$$ are some perturbations.

Keywords: Jacobi matrices, double root case, asymptotic behavior, subordination theory, absolutely continuous spectrum, discrete spectrum.

Mathematics Subject Classification: 39A10, 39A70, 47B36, 47B25.

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• Wojciech Motyka
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland
• Communicated by S.N. Naboko.
• Revised: 2014-04-06.
• Accepted: 2014-04-08.
• Published online: 2014-12-15.