The asymptotic properties of the spectrum of nonsymmetrically perturbed Jacobi matrix sequences

Journal of Approximation Theory

Volumn 144, Issue 1, 2007, Pages 84-102

  Golinskii, Leonid ^a   Serra Capizzano, Stefano ^b  

^a B VERKIN INSTITUTE FOR LOW TEMPERATURE PHYSICS AND ENGINEERING   (Ukraine)

^b UNIVERSITY OF INSUBRIA   (Italy)

Author keywords

GLT sequence; Jacobi matrix; Joint eigenvalue distribution; Matrix sequence; Mergelyan Theorem

Indexed keywords

EID: 33751322378     PISSN: 00219045     EISSN: 10960430     Source Type: Journal    
DOI: 10.1016/j.jat.2006.05.002     Document Type: Article

References (21)

1. Barrios D., López G., Martínez-Finkelshtein A., and Torrano E. On the domain of convergence and poles of complex J-fractions. J. Approx. Theory 93 (1998) 177-200
2. Barrios D., López G., Martínez-Finkelshtein A., and Torrano E. The finite dimensional approximation of the resolvent of infinite banded matrix and continuous fractions. Mat. Sb. 190 (1999) 23-42
3. Bhatia R. Matrix Analysis (1997), Springer, New York
4. Bhatia R. Pinching, trimming, truncating, and averaging of matrices. Amer. Math. Monthly 107 (2000) 602-608
5. Fasino D., and Serra-Capizzano S. From Toeplitz matrix sequences to zero distribution of orthogonal polynomials. Contemp. Math. 323 (2003) 329-340
6. Geronimo J.S., Harrell II E.M., and Van Assche W. On the asymptotic distribution of eigenvalues of banded matrices. Constr. Approx. 4 (1988) 403-417
7. Golinskii L. On the spectra of infinite Hessenberg and Jacobi matrices. Matematicheskaya Fizika, Analiz, Geometriya 7 (2000) 284-298
8. Hladnik M., Holbrook J., and Serra-Capizzano S. Fat diagonals and Fourier analysis. SIAM J. Matrix Anal. Appl. 24 4 (2003) 1060-1070
9. S. Holmgren, S. Serra-Capizzano, P. Sundqvist, Can one hear the composition of a drum? Mediterr. J. Math., to appear.
10. Killip R., and Simon B. Sum rules for Jacobi matrices and their applications to spectral theory. Ann. Math. 158 (2003) 253-321
11. Kuijlaars A.B.J., and Serra-Capizzano S. Asymptotic zero distribution of orthogonal polynomials with discontinuously varying recurrence coefficients. J. Approx. Theory 113 (2001) 142-155
12. Máté A., Nevai P., and Van Assche W. The support of measures associated with orthogonal polynomials and the spectra of related self-adjoint operators. Rocky Mountain J. Math. 21 (1991) 501-527
13. Nevai P. Géza Freud, orthogonal polynomials and Christoffel functions, A case study. J. Approx. Theory 48 (1986) 3-167
14. Rudin W. Real and Complex Analysis (1974), McGraw-Hill, New York
15. Serra-Capizzano S. Spectral behavior of matrix sequences and discretized boundary value problems. Linear Algebra Appl. 337 (2001) 37-78
16. Serra-Capizzano S. Generalized locally Toeplitz sequences: spectral analysis and applications to discretized partial differential equations. Linear Algebra Appl. 366 1 (2003) 371-402
17. S. Serra-Capizzano, The GLT class as a Generalized Fourier Analysis and applications, Technical Report, SCCM-05-07, Stanford University 2005, Linear Algebra Appl., to appear.
18. Stahl H., and Totik V. General orthogonal polynomials. Encyclopedia of Mathematics and its Applications vol. 43 (1992), Cambridge University Press, New York
19. Tilli P. A note on the spectral distribution of Toeplitz matrices. Linear Multilinear Algebra 45 (1998) 147-159
20. Tilli P. Some results on complex Toeplitz eigenvalues. J. Math. Anal. Appl. 239 2 (1999) 390-401
21. Van Assche W. Zero distribution of orthogonal polynomials with asymptotically periodic varying recurrence coefficients. In: Priezzhev V.B., and Spiridonov V.P. (Eds). Self-Similar Systems (1999), Joint Institute for Nuclear Research, Dubna, Russia 392-402