Spectra of some selfadjoint Jacobi operators in the double root case

• Autorzy: Motyka W.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2015.35.3.353

• Języki publikacji: EN

Abstrakty

EN

In this paper we prove a mixed spectrum of Jacobi operators defined by λn = s(n)(1 + x(n)) and qn = — 2s(n)(l+y/(n)), where (s(n)) is a real unbounded sequence, (x(n)) and (y(n)) are some perturbations.

Słowa kluczowe

EN

Jacobi matrices; double root case; asymptotic behavior; subordination theory; absolutely continuous spectrum; discrete spectrum

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2015
• Tom: Vol. 35, no. 3
• Strony: 353--370
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Motyka W.

• AGH University of Science and Technology Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Krakow, Poland

Bibliografia

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• [2] J.M. Holte, Properties of O-regularly Varying Sequences: Elementary Proofs, Interna­tional Congress ol Mathematicians, Beijing, 2002.
• [3] J. Janas, The asymptotic analysis of generalized eigenvectors of some Jacobi operators - Jordan box case, J. Difference Equ. Appl. 12 (2006), 597-618.
• [4] J. Janas, M. Moszyński, Alternative approaches to the absolute continuity of Jacobi ma­trices with monotonie weights, Integral Equations Operator Theory 43 (2002), 397-416.
• [5] J. Janas, S. Naboko, Multitreshold spectral phase transitions for a class of Jacobi ma­trices, Oper. Theory Adv. Appl. 124 (2001), 267-285.
• [6] J. Janas, S. Naboko, Spectral properties of self adjoint Jacobi matrices coming from birth and death processes, Oper. Theory Adv. Appl. 127 (2001), 387-397.
• [7] J. Janas, S. Naboko, E. Sheronova, Asymptotic behavior of generalized eigenvectors of Jacobi matrices in the critical ("double root") case, Journal for Analysis and its Applications 28 (2009), 411-430.
• [8] S. Khan, D.B. Pearson, Subordinacy and spectral theory for infinite matrices, Helv. Phys. Acta 65 (1992), 505-527.
• [9] M. Moszyński, Non-existence of subordinate solutions for Jacobi operators in some critical cases, Integral Equations Operator Theory 75 (2013), 363-392.
• [10] W. Motyka, The asymptotic analysis of a class of self-adjoint second-order difference equations: Jordan box case, Glasg. Math. J. 51 (2009), 109-125.
• [11] W. Motyka, Spectral phase transition for a class of power-like Jacobi matrices, Acta Sci. Math. (Szeged) 76 (2010), 443-469.
• [12] W. Motyka, Self adjoint second order difference equations with unbounded coefficients in the double root case, to appear in J. Difference Equ. Appl.