Opuscula Math. 35, no. 3 (2015), 353-370
Spectra of some selfadjoint Jacobi operators in the double root case
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.