Asymptotic expansion of large eigenvalues for a class of unbounded Jacobi matrices

Abstract

We investigate a class of infinite tridiagonal matrices which define unbounded self-adjoint operators with discrete spectrum. Our purpose is to establish the asymptotic expansion of large eigenvalues and to compute two correction terms explicitly.

Keywords

• tridiagonal matrix
• band matrix
• unbounded self-adjoint operator
• discrete spectrum
• large eigenvalues
• asymptotics