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.

UDC: 519.61

Received: 13.10.2006
Revised: 09.11.2006

DOI: 10.4213/mzm3724

 English version: Mathematical Notes, 2007, 81:5, 628–631

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