Opuscula Math. 35, no. 3 (2015), 353-370

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.
  • Received: 2013-09-15.
  • Revised: 2014-04-06.
  • Accepted: 2014-04-08.
  • Published online: 2014-12-15.
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Cite this article as:
Wojciech Motyka, Spectra of some selfadjoint Jacobi operators in the double root case, Opuscula Math. 35, no. 3 (2015), 353-370, http://dx.doi.org/10.7494/OpMath.2015.35.3.353

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