Asymptotics of large eigenvalues for some discrete unbounded Jacobi matrices

作者：Malejki Maria^*

来源：Linear Algebra and Its Applications, 2009, 431(10): 1952-1970.

DOI：10.1016/j.laa.2009.06.035

• Tridiagonal matrix
• Jacobi matrix
• Self-adjoint operator
• Asymptotics
• Eigenvalue
• Point spectrum

The aim of this paper is to find asymptotic formulas for eigenvalues of self-adjoint discrete operators in l2(N) given by some infinite symmetric Jacobi matrices. The approach used to calculate an asymptotic behaviour of eigenvalues is based on method of diagonalization, Janas and Naboko's lemma [J.Janas, S. Naboko, Infinite Jacobi matrices with unbounded entries: asymptotics of eigenvalues and the transformation operator approach, SIAM J. Math. Anal. 36 (2) (2004) 643-658] and the Rozenbljunn theorem [G.V. Rozenbijum, Near-similarity of operators and the spectral asymptotic behaviour of pseudodifferential operators on the circle, (Russian) Trudy Maskov. Mat, Obshch. 36 (1978) 59-84]. The asymptotic formulas are given with use of eigenvalues and determinants of finite tridiagonal matrices.

• 出版日期2009-10-15