On the error estimates for the Rayleigh-Schrödinger series and the Kato-Rellich perturbation series

Journal of the Australian Mathematical Society

Rekha P. Kulkarni¹ 

[1] Balmohan V. Limaye

关键词: 41 A 25;    41 A 35;    41 A 65;    47 A 70;   

DOI  :  10.1017/S1446788700030937

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let λ be a simple eigenvalue of a bounded linear operator T on a Banach space X, and let (Tn) be a resolvent operator approximation of T. For large n, let Sn denote the reduced resolvent associated with Tn and λn, the simple eigenvalue of Tn near λ. It is shown thatunder the assumption that all the spectral points of T which are nearest to λ belong to the discrete spectrum of T. This is used to find error estimates for the Rayleigh-Schrödinger series for λ and ϕ with initial terms λn and ϕn, where P (respectively, ϕn) is an eigenvector of T (respectively, Tn) corresponding to λ (respectively, λn), and for the Kato-Rellich perturbation series for PPn, where P (respectively, Pn) is the spectral projection for T (respectively, Tn) associated with λ (respectively, λn).

【 授权许可】

Unknown