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Abstrakty
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.
Wydawca
Rocznik
Tom
Strony
39--51
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
autor
autor
- Department of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland, cojuhari@uci.agh.edu.pl
Bibliografia
- [1] N. I. Akhiezer, Infinite matrices and moment problem, Uspekhi Mat. Nauk 9 (1941), 126-156.
- [2] -, The Classical Moment Problem, Oliver and Boyd, Edinburgh, 1965.
- [3] Yu. M. Berezanskii, Expansions in Eigenfunctions of Self-Adjoint Operators, Transl. Math. Monogr. 17, Amer. Math. Soc., Providence, RI, 1968.
- [4] R. Carey and J. Pincus, Unitary equivalence modulo trace class for self-adjoint operators, Amer. J. Math. 98 (1976), 481-514.
- [5] P. Cojuhari and J. Janas, Discreteness of the spectrum for some unbounded Jacobi matrices, Acta Math. Sci. 73 (2007), 649-667.
- [6] J. Dombrowski, J. Janas, M. Moszyński and S. Pedersen, Spectral gaps resulting from periodic perturbations of a class of Jacobi operators, Constr. Approx. 20 (2004), 585-601.
- [7] J. Dombrowski and S. Pedersen, Absolute continuity for Jacobi matrices with constant row sums, J. Math. Anal. Appl. 277 (2002), 695-713.
- [8] J. Janas and S. Naboko, Jacobi matrices with power like weights-grouping in blocks approach, J. Punct. Anal. 166 (1999), 218-243.
- [9] -, -, Spectral analysis of selfadjoint Jacobi matrices with periodically modulated entries, ibid. 191 (2002), 318-342.
- [10] J. Janas, S. Naboko and G. Stolz, Spectral theory for a class of periodically perturbed unbounded Jacobi matrices: elementary methods, J. Comput. Appl. Math. 171 (2004), 265-276.
- [11] T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1966.
- [12] S. Khan and D. Pearson, Subordinacy and spectral theory for infinite matrices, Helv. Phys. Acta 65 (1992), 505-527.
- [13] D. Pearson, Singular continuous measures in scattering theory, Comm. Math. Phys. 60 (1978), 13-36.
- [14] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1, Academic Press, New York, 1972.
- [15] B. Simon, Operators with singular continuous spectrum, I. General operators, Ann. of Math. 141 (1995), 131-145.
- [16] -, Orthogonal Polynomials on the Unit Circle, Part 2: Spectral Theory, Colloq. Publ. 54, Amer. Math. Soc., Providence, RI, 2005.
- [17] B. Simon and T. Spencer, Trace class perturbations and the absence of absolutely continuous spectra, Comm. Math. Phys. 125 (1989), 113-125.
- [18] B. Simon and G. Stolz, Operators with singular continuous spectrum V. Sparse potentials, Proc. Amer. Math. Soc. 124 (1996), 2073-2080.
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Bibliografia
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bwmeta1.element.baztech-article-BAT5-0029-0005