ACTA issues

Spectral phase transition for a class of power-like Jacobi matrices

Wojciech Motyka

Acta Sci. Math. (Szeged) 76:3-4(2010), 443-469

Abstract. In this paper we discuss the spectral properties of a class of Jacobi operators defined by $\lambda_n=n^{\alpha }+c_n$ and $q_n=-2n^{\alpha }+b_n$, where $(c_n)$ and $(b_n)$ are real two-periodic sequences. From the asymptotic behavior of the solutions of the generalized eigenequation, which is in the double root case, a mixed spectrum is obtained.

AMS Subject Classification (1991): 39A10, 47B25

Keyword(s): Jacobi matrices, double root case, asymptotic behavior, subordination theory, absolutely continuous spectrum, discrete spectrum

Received July 31, 2008, and in final form March 12, 2010. (Registered under 73/2010.)