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On the Common Part of the Spectrum of Finite Difference Operators Generated by Systems of Polynomials
E. V. Zakharova State University – Higher School of Economics, Nizhny Novgorod Branch
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.
Keywords:
multiple orthogonality polynomials, difference operators, essential spectrum, Hessenberg matrix, Hardy space, Toeplitz operator.
Received: 13.10.2006 Revised: 09.11.2006
Citation:
E. V. Zakharova, “On the Common Part of the Spectrum of Finite Difference Operators Generated by Systems of Polynomials”, Mat. Zametki, 81:5 (2007), 703–706; Math. Notes, 81:5 (2007), 628–631
Linking options:
https://www.mathnet.ru/eng/mzm3724https://doi.org/10.4213/mzm3724 https://www.mathnet.ru/eng/mzm/v81/i5/p703
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