Asymptotics of the discrete spectrum for complex Jacobi matrices

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