Displaying similar documents to “Spectral Theory for Slowly Oscillating Potentials I. Jacobi Matrices.”

Spectral transition parameters for a class of Jacobi matrices

Joanne Dombrowski, Steen Pedersen (2002)

Studia Mathematica

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This paper initially considers a class of unbounded Jacobi matrices defined by an increasing sequence of repeated weights. Spectral parameters are then introduced in various ways to allow the authors to study the nature and location of the spectrum as a function of these parameters.

Unbounded Jacobi Matrices with Empty Absolutely Continuous Spectrum

Petru Cojuhari, Jan Janas (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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Sufficient conditions for the absence of absolutely continuous spectrum for unbounded Jacobi operators are given. A class of unbounded Jacobi operators with purely singular continuous spectrum is constructed as well.

On the completely indeterminate case for block Jacobi matrices

Andrey Osipov (2017)

Concrete Operators

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We consider the infinite Jacobi block matrices in the completely indeterminate case, i. e. such that the deficiency indices of the corresponding Jacobi operators are maximal. For such matrices, some criteria of complete indeterminacy are established. These criteria are similar to several known criteria of indeterminacy of the Hamburger moment problem in terms of the corresponding scalar Jacobi matrices and the related systems of orthogonal polynomials.

Slowly oscillating perturbations of periodic Jacobi operators in l²(ℕ)

Marcin Moszyński (2009)

Studia Mathematica

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We prove that the absolutely continuous part of the periodic Jacobi operator does not change (modulo unitary equivalence) under additive perturbations by compact Jacobi operators with weights and diagonals defined in terms of the Stolz classes of slowly oscillating sequences. This result substantially generalizes many previous results, e.g., the one which can be obtained directly by the abstract trace class perturbation theorem of Kato-Rosenblum. It also generalizes several results concerning...