Abstract
This paper explores the relationship between the spectra of perturbed infinite banded Laurent matricesL(a)+K and their approximations by perturbed circulant matricesC n (a)+P n KP n for largen. The entriesK jk of the perturbation matrices assume values in prescribed sets Ω jk at the sites (j, k) of a fixed finite setE, and are zero at the sites (j, k) outsideE. WithK Ω denoting the ensemble of these perturbation matrices, it is shown that $$\mathop {\lim }\limits_{n \to \infty } \bigcup\limits_{K \in K_\Omega ^E } {{\text{sp}}} {\text{ }}(C_n (a) + P_n KP_n ) = \bigcup\limits_{K \in K_\Omega ^E } {{\text{sp}}} {\text{ (}}L(a) + K)$$ under several fairly general assumptions onE and Ω.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callSimilar Papers
More From: Integral Equations and Operator Theory
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
