THE ASYMPTOTIC ANALYSIS OF A CLASS OF SELF-ADJOINT SECOND-ORDER DIFFERENCE EQUATIONS: JORDAN BOX CASE
Glasgow mathematical journal, Tome 51 (2009) no. 1, pp. 109-125

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper, we are computing asymptotic formulas for a base of solutions of the second-order difference equations in the double root case. Two methods are presented.
DOI : 10.1017/S0017089508004709
Mots-clés : 39A10, 47B25
MOTYKA, WOJCIECH. THE ASYMPTOTIC ANALYSIS OF A CLASS OF SELF-ADJOINT SECOND-ORDER DIFFERENCE EQUATIONS: JORDAN BOX CASE. Glasgow mathematical journal, Tome 51 (2009) no. 1, pp. 109-125. doi: 10.1017/S0017089508004709
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[1] 1.Elaydi, S. N., An introduction to difference equations (Springer Verlag New York, 1999). Google Scholar | DOI

[2] 2.Hall, L. M. and Trimble, S. Y., Asymptotic behavior of solutions of Poincare difference equations, in Proceedings of the International Conference of Theory and Applications of Differential Equations (Aftabizadeh, A.R., editor) (Ohio University, Ohio, 1988), 412–416. Google Scholar

[3] 3.Janas, J., The asymptotic analysis of generalized eigenvectors of some Jacobi operators. Jordan box case, J. Difference Eq. Appl. 12 (6) (2006), 597–618. Google Scholar | DOI

[4] 4.Janas, J. and Naboko, S., Spectral properties of selfadjoint Jacobi matrices coming from birth and death processes, Operator Theory: Adv. Appl. 127 (2001), 387–397. Google Scholar

[5] 5.Janas, J., Naboko, S. and Sheronova, E., Asymptotic behavior of generalized eigenvectors of Jacobi matrices in the critical (“double root”) case, (in press). Google Scholar

[6] 6.Kelley, W., Asymptotic analysis of solutions in the “Double Root” case, Comput. Math. Appl. 28 (1994), 167–173. Google Scholar | DOI

[7] 7.Khan, S. and Pearson, D. B., Subordinacy and spectral theory for infinite matrices, Helv. Phys. Acta 65 (1992), 505–527. Google Scholar

[8] 8.Kooman, R. J., Asymptotic behavior of solutions of linear recurrences and sequences of Möbius-transformations, J. Approx. Theory 93 (1998), 1–58. Google Scholar | DOI

[9] 9.Simonov, S., An example of spectral phase transition phenomenon in a class of Jacobi matrices with periodically modulated weights, Operator Theory: Adv. Appl. 174 (2007), 187–203. Google Scholar

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