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.
Günter Stolz (1994)
Manuscripta mathematica
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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.
Pierre van Moerbeke (1976)
Inventiones mathematicae
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William B. Gragg, William J. Harrod (1984)
Numerische Mathematik
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K. Veselic (1979)
Numerische Mathematik
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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...
M. Arioli, F. Romani (1985)
Numerische Mathematik
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Jan Janas, Marcin Moszyński (2012)
Studia Mathematica
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We describe the spectra of Jacobi operators J with some irregular entries. We divide ℝ into three “spectral regions” for J and using the subordinacy method and asymptotic methods based on some particular discrete versions of Levinson’s theorem we prove the absolute continuity in the first region and the pure pointness in the second. In the third region no information is given by the above methods, and we call it the “uncertainty region”. As an illustration, we introduce and analyse the...
K. Veselic, H.J. Wenzel (1979)
Numerische Mathematik
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K. Veselic (1975/76)
Numerische Mathematik
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Wojciech Motyka (2007)
Colloquium Mathematicae
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This work deals with a class of Jacobi matrices with power-like weights. The main theme is spectral analysis of matrices with zero diagonal and weights where α ∈ (0,1]. Asymptotic formulas for generalized eigenvectors are given and absolute continuity of the matrices considered is proved. The last section is devoted to spectral analysis of Jacobi matrices with qₙ = n + 1 + (-1)ⁿ and .