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Absolutely continuous Jacobi operators

Authors:	Steen Pedersen

Institution:	Department of Mathematics, Wright State University, Dayton, Ohio 45435

Abstract:	We show (among other results) that a symmetric Jacobi matrix whose diagonal is the zero sequence and whose super-diagonal satisfies $h_{2n-1}=h_{2n}$ , $h_k\leq h_{k+1}$ and $0<b\leq\tfrac{h_{2k+2}}{k+1}\leq\tfrac{h_{2k}}{k}$ has purely absolutely continuous spectrum when considered as a self-adjoint operator on $\ell^2(\mathbb{N} )$ .

Keywords:	Orthogonal polynomials weighted shift absolute continuity Jacobi matrix

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