Opuscula Math. 34, no. 1 (2014), 139-160
http://dx.doi.org/10.7494/OpMath.2014.34.1.139

Opuscula Mathematica

# Asymptotics of the discrete spectrum for complex Jacobi matrices

Maria Malejki

Abstract. The spectral properties and the asymptotic behaviour of the discrete spectrum for a special class of infinite tridiagonal matrices are given. We derive the asymptotic formulae for eigenvalues of unbounded complex Jacobi matrices acting in $$l^2(\mathbb{N})$$.

Keywords: tridiagonal matrix, complex Jacobi matrix, discrete spectrum, eigenvalue, asymptotic formula, unbounded operator, Riesz projection.

Mathematics Subject Classification: 47B36, 47B37, 47B06, 47A75, 15A18.

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• Maria Malejki
• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland
• Revised: 2013-12-04.
• Accepted: 2013-12-04.