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Zbl 0944.34018
Brown, B.M.; McCormack, D.K.R.; Evans, W.D.; Plum, M.
On the spectrum of second-order differential operators with complex coefficients. (English)
[J] Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 455, No.1984, 1235-1257 (1999). ISSN 1364-5021; ISSN 1471-2946/e

An extension of the Weyl limit-point, limit-circle classification for the Sturm-Liouville equation with a complex-valued potential on $[a,b)$, where $-\infty<a<b\leq\infty$ and $a$ and $b$ are the endpoints regular and singular, respectively, was obtained by {\it A. R. Sims} [J. Math. Mech., Vol. 6, 247-285 (1957; Zbl 0077.29201)]. The authors establish an analogue of the Sims theory to the equation $$ -(py')'+qy=\lambda wy, $$ where $p$ and $q$ are complex-valued, and $w$ is a positive weight function. An $m$-function is constructed and a relationship between its properties and the spectrum of corresponding $m$-accretive operators is analysed.
[Vyacheslav Pivovarchik (Odessa)]

MSC 2000:: *34B24 Sturm-Liouville theory
34M15 Algebraic aspects of differential equations in the complex domain

Keywords: Sturm-Liouville problems; spectral theory; Titchmarsh-Weyl-Sims theory

Citations: Zbl 0077.29201

Cited in: Zbl pre06122148 Zbl 1241.34031 Zbl 1228.34045 Zbl 1240.34145 Zbl 1145.47303 Zbl 1055.34048

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