Abstract
In this paper, we study the spectra of finite difference operators generated by systems of multiple orthogonal polynomials and the corresponding systems of measures of Stieltjes type. We show that the common support of the orthogonality measures coincides with the intersection of the spectra of the family of finite difference operators with common collection of Weyl functions.
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References
E. M. Nikishin and V. N. Sorokin, Rational Approximations and Orthogonality (Nauka, Moscow, 1988) [in Russian].
A. I. Aptekarev and V. A. Kaliaguine, “Complex rational approximation and difference operators,” Rend. Circ. Mat. Palermo (2) Suppl., Vol. I, Acquafredda di Maratea, No. 52, 3–21 (1998).
V. A. Kalyagin, “Hermite-Padé approximants and spectral analysis of nonsymmetric operators,” Mat. Sb. 185(6), 79–100 (1994) [Russian Acad. Sci. Sb. Math. 82 (1), 199–216 (1995)].
B. Beckermann and V. Kaliaguine, “Diagonal of the Padé table and the approximation of the Weyl function of second-order difference operator,” Constr. Approx. 13(4), 481–510 (1997).
A. Aptekarev, V. Kaliaguine, and J. Van Iseghem, “Genetic sum representations for the moments of Stieltjes functions and their applications,” Constr. Approx. 16(4), 487–524 (2000).
A. Aptekarev, V. Kalyagin, G. Lopez, and I. Rocha, “On the limit behavior of recurrence coefficients for multiple orthogonal polynomials,” J. Approx. Theory 139(1–2), 346–370 (2006).
J. Gilewicz and E. Zakharova, Le spectre de l’opérateur complexe périodique de Jacobi dans l 2 (N), Preprint no. 4167 (CPT, Luminy, 2000).
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Original Russian Text © E. V. Zakharova, 2007, published in Matematicheskie Zametki, 2007, Vol. 81, No. 5, pp. 703–706.
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Zakharova, E.V. On the common part of the spectrum of finite difference operators generated by systems of polynomials. Math Notes 81, 628–631 (2007). https://doi.org/10.1134/S0001434607050070
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DOI: https://doi.org/10.1134/S0001434607050070