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Non-self-adjoint difference operators and their spectrum

Wilson, Robert 2005. Non-self-adjoint difference operators and their spectrum. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461 (2057) , pp. 1505-1531. 10.1098/rspa.2004.1416

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Initially, this paper is a discrete analogue of the work of Brown et al. (1999 Proc. R. Soc. A 455, 1235–1257) on second-order differential equations with complex coefficients. That is, we investigate the general non-self-adjoint second-order difference expression [formula] where the coefficients pn and qn are complex and Δ is the forward difference operator, i.e. Δxn=xn+1−xn. Properties of the so-called Hellinger–Nevanlinna m-function for the recurrence relation Mxn=λwnxn, where the wn are real and positive, are examined, and relationships between the properties of the m-function and the spectrum of the associated operator are explored. However, an essential difference between the continuous and the discrete case arises in the way in which we define the operator natural to the problem. Nevertheless, analogous results regarding the spectrum of this operator are obtained.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: difference operators; spectral theory; Hellinger–Nevanlinna m-function; limit circle; limit point
Publisher: Royal Society
ISSN: 1364-5021
Last Modified: 05 Sep 2020 01:38

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