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Matematicheskie Zametki, 2007, Volume 81, Issue 5, Pages 703–706
DOI: https://doi.org/10.4213/mzm3724 (Mi mzm3724) 		 
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
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DOI: https://doi.org/10.4213/mzm3724
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
English version:
Mathematical Notes, 2007, Volume 81, Issue 5, Pages 628–631
DOI: https://doi.org/10.1134/S0001434607050070
Bibliographic databases:
UDC: 519.61
Language: Russian
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
Citation in format AMSBIB
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