Approximation in eigenvalue problems for holomorphic fredholm operator functions Ii (Convergence Rate)

Abstract

In this paper we prove some asymptotic error estimations for the difference of eigenvalues of a holomorphic operator function and its approximations. We assume the discrete approximation scheme of F. Stummel [12] for spaces and the regular approximation scheme for operator functions.

To get error estimations two approaches are used in this paper. In Sections 2.1 and 2.2 the problem is reduced to the case of matrix functions by the construction, presented in [11]. Here we follow the approach of [4, 5, 6, 8, 9, 10]. Some notations and results of [11] are briefly recalled in Paragraph 1.

In Section 2.3, the estimation is derived by transforming of an appropriately chosen identity. Here we follow [15, 16].