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On the spectrum of second-order differential operators with complex coefficients. (English) Zbl 0944.34018
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.

34B24Sturm-Liouville theory
34M15Algebraic aspects of ODE in the complex domain
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