About essential spectra of unbounded Jacobi matrices

Journal of Approximation Theory - Tập 278 - Trang 105746 - 2022
Grzegorz Świderski1,2, Bartosz Trojan3
1Department of Mathematics, KU Leuven, Celestijnenlaan 200B box 2400, BE-3001 Leuven, Belgium
2University of Wrocław, Faculty of Mathematics and Computer Science, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
3Instytut Matematyczny Polskiej Akademii Nauk, ul. Śniadeckich 8, 00-696 Warszawa, Poland

Tài liệu tham khảo

Boutet de Monvel, 2011, Unbounded Jacobi matrices with a few gaps in the essential spectrum: constructive examples, Integr. Equ. Oper. Theory, 69, 151, 10.1007/s00020-010-1856-x Breuer, 2010, Spectral and dynamical properties of certain random Jacobi matrices with growing parameters, Trans. Amer. Math. Soc., 362, 3161, 10.1090/S0002-9947-10-04856-7 Chihara, 1962, Chain sequences and orthogonal polynomials, Trans. Amer. Math. Soc., 104, 1, 10.1090/S0002-9947-1962-0138933-7 Damanik, 2007, Unbounded Jacobi matrices at critical coupling, J. Approx. Theory, 145, 221, 10.1016/j.jat.2006.09.002 Dombrowski, 2004, Eigenvalues and spectral gaps related to periodic perturbations of Jacobi matrices, vol. 154, 91 Dombrowski, 2009, Jacobi matrices: Eigenvalues and spectral gaps, vol. 186, 103 Dombrowski, 2004, Spectral gaps resulting from periodic perturbations of a class of Jacobi operators, Constr. Approx., 20, 585, 10.1007/s00365-003-0544-3 Dombrowski, 1995, Orthogonal polynomials, spectral measures, and absolute continuity, J. Comput. Appl. Math., 65, 115, 10.1016/0377-0427(95)00104-2 Dombrowski, 2002, Absolute continuity for unbounded Jacobi matrices with constant row sums, J. Math. Anal. Appl., 267, 695, 10.1006/jmaa.2001.7808 Dombrowski, 2002, Spectral transition parameters for a class of Jacobi matrices, Studia Math., 152, 217, 10.4064/sm152-3-2 Hinton, 1978, Spectral analysis of second order difference equations, J. Math. Anal. Appl., 63, 421, 10.1016/0022-247X(78)90088-4 Janas, 2003, Spectral properties of Jacobi matrices by asymptotic analysis, J. Approx. Theory, 120, 309, 10.1016/S0021-9045(02)00038-2 Janas, 2006, New discrete levinson type asymptotics of solutions of linear systems, J. Differ Equ. Appl., 12, 133, 10.1080/10236190500489897 Janas, 2012, Spectral analysis of unbounded Jacobi operators with oscillating entries, Studia Math., 209, 107, 10.4064/sm209-2-2 Janas, 2001, Multithreshold spectral phase transitions for a class of Jacobi matrices, vol. 124, 267 Janas, 2001, Spectral properties of selfadjoint Jacobi matrices coming from birth and death processes, vol. 127, 387 Janas, 2002, Spectral analysis of selfadjoint Jacobi matrices with periodically modulated entries, J. Funct. Anal., 191, 318, 10.1006/jfan.2001.3866 Janas, 2009, Asymptotic behavior of generalized eigenvectors of Jacobi matrices in the critical (”double root”) case, Z. Anal. Anwend., 28, 411, 10.4171/ZAA/1391 Janas, 2004, Spectral theory for a class of periodically perturbed unbounded Jacobi matrices: elementary methods, J. Comput. Appl. Math., 171, 265, 10.1016/j.cam.2004.01.023 Khan, 1992, Subordinacy and spectral theory for infinite matrices, Helv. Phys. Acta, 65, 505 Kostyuchenko, 1999, Generalized Jacobi matrices and deficiency indices of ordinary differential operators with polynomial coefficients, Funct. Anal. Appl., 33, 25, 10.1007/BF02465140 Moszyński, 2009, Slowly oscillating perturbations of periodic Jacobi operators in l2(N), Studia Math., 192, 259, 10.4064/sm192-3-4 Motyka, 2015, Spectra of some selfadjoint Jacobi operators in the double root case, Opuscula Math., 35, 353, 10.7494/OpMath.2015.35.3.353 Naboko, 2009, Discrete spectrum in a critical coupling case of Jacobi matrices with spectral phase transitions by uniform asymptotic analysis, J. Approx. Theory, 161, 314, 10.1016/j.jat.2008.09.005 Naboko, 2010, Spectral analysis of a class of Hermitian Jacobi matrices in a critical (double root) hyperbolic case, Proc. Edinb. Math. Soc. (2), 53, 239, 10.1017/S001309150700106X Naboko, 2021, Titchmarsh–Weyl formula for the spectral density of a class of Jacobi matrices in the critical case, Funct. Anal. Appl., 55, 94, 10.1134/S0016266321020027 Sahbani, 2016, On the spectrum of periodic perturbations of certain unbounded Jacobi operators, Opuscula Math., 36, 807, 10.7494/OpMath.2016.36.6.807 Schmüdgen, 2017, vol. 277 Silva, 2004, Uniform Levinson type theorem for discrete linear systems, Oper. Theory Adv. Appl., 154, 203 Silva, 2007, Uniform and smooth Benzaid–Lutz type theorems and applications to Jacobi matrices, Oper. Theory Adv. Appl., 174, 173 Silva, 2007, Jacobi matrices with rapidly growing weights having only discrete spectrum, J. Math. Anal. Appl., 328, 1087, 10.1016/j.jmaa.2006.06.005 Simon, 2010, 664 Simonov, 2007, An example of spectral phase transition phenomenon in a class of Jacobi matrices with periodically modulated weights, 187 Stolz, 1994, Spectral theory for slowly oscillating potentials I. Jacobi matrices, Manuscripta Math., 245, 10.1007/BF02567456 Świderski, 2017, Periodic perturbations of unbounded Jacobi matrices II: Formulas for density, J. Approx. Theory, 216, 67, 10.1016/j.jat.2017.01.004 Świderski, 2018, Periodic perturbations of unbounded Jacobi matrices III: The soft edge regime, J. Approx. Theory, 233, 1, 10.1016/j.jat.2018.04.006 Świderski, 2020, Spectral properties of some complex Jacobi matrices, Integr. Equ. Oper. Theory, 92, 10.1007/s00020-020-2569-4 Świderski, 2017, Periodic perturbations of unbounded Jacobi matrices I: Asymptotics of generalized eigenvectors, J. Approx. Theory, 216, 38, 10.1016/j.jat.2017.01.003 Świderski, 2020, Asymptotics of orthogonal polynomials with slowly oscillating recurrence coefficients, J. Funct. Anal., 278, 10.1016/j.jfa.2019.108326 Świderski, 2021, Asymptotic behavior of Christoffel-Darboux kernel via three-term recurrence relation II, J. Approx. Theory, 261, 10.1016/j.jat.2020.105496 Świderski, 2021, Asymptotic behaviour of Christoffel-Darboux kernel via three-term recurrence relation I, Constr. Approx., 54, 49, 10.1007/s00365-020-09519-w Szwarc, 2002, Absolute continuity of spectral measure for certain unbounded Jacobi matrices, 255