On the spectrum of periodic perturbations of certain unbounded Jacobi operators

• Autorzy: Sahbani J.

Identyfikatory

DOI

10.7494/OpMath.2016.36.6.807

• Języki publikacji: EN

Abstrakty

EN

It is known that a purely off-diagonal Jacobi operator with coefficients [formula] has a purely absolutely continuous spectrum filling the whole real axis. We show that a 2-periodic perturbation of these operators creates a non trivial gap in the spectrum.

Słowa kluczowe

EN

essential spectrum; spectral gap; periodic perturbation

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2016
• Tom: Vol. 36, no. 6
• Strony: 807--818
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Sahbani J.

• Universite Paris Diderot Institut de Mathematiques de Jussieu-Paris Rive Gauche-UMR7586 Batiment Sophie Germain-case 7012 5 rue Thomas Mann, 75205 Paris Cedex 13, France

Bibliografia

• [1] Yu.M. Berezanskii, Expansions in Eigenfunctions of Selfadjoint Operators, vol. 17, Translation of Mathematical Monographs, Amer. Math. Soc, Providence, RI, 1968.
• [2] J. Dombrowski, J. Janas, M. Moszyński, S. Pedersen, Spectral gaps resulting from periodic perturbations of a class of Jacobi operators, Constr. Approx. 20 (2004) 4, 585-601.
• [3] J. Dombrowski, S. Pedersen, Absolute continuity for Jacobi matrices with constant row sums, J. Math. Anal. Appl. 267 (2002), 695-713.
• [4] J. Dombrowski, S. Pedersen, Spectral transition parameters for a class of Jacobi matrices, Studia Math. 152 (2002), 217-229.
• [5] D.B. Hinton, R.T. Lewis, Spectral analysis of second-order difference equations, J. Math. Anal. Appl. 63 (1978), 421-438.
• [6] J. Janas, S.N. Naboko, Jacobi matrices with power-like weight grouping in blocks approach, J. Func. Anal. 166 (1999), 218-243.
• [7] J. Janas, S.N. Naboko, Multi-threshold spectral phase transitions for a class of Jacobi matrices, Operator Theory: Adv. Appl. 124 (2001), 267-285.
• [8] J. Janas, S. Naboko, G. Stolz, Spectral theory for a class of periodically perturbed unbounded Jacobi matrices: elementary methods, J. Comput. Appl. Math. 171 (2004) 1-2, 265-276.
• [9] J. Janas, S. Naboko, G. Stolz, Decay bounds on eigenfunctions and the singular spectrum, of unbounded Jacobi matrices, Int. Math. Res. Not. IMRN (2009), no. 4, 736-764.
• [10] M. Moszynski, Spectral properties of some Jacobi matrices with double weights, J. Math. Anal. Appl. 280 (2003), 400-412.
• [11] S. Pedersen, Absolutely continuous Jacobi operators, Proc. Amer. Math. Soc. 130 (2002), 2369-2376.
• [12] J. Sahbani, Spectral properties of Jacobi matrices of certain birth and death processes, J. Operator Theory 56 (2006) 2, 377-390.
• [13] J. Sahbani, Spectral theory of certain unbounded Jacobi matrices, J. Math. Anal. Appl. 342 (2008) 1, 663-681.
• [14] J. Sahbani, Spectral theory of a class of block Jacobi matrices and applications, J. Math. Anal. Appl. 438 (2016) 1, 93-118.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.