## 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 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.

### MSC:

 34B24 Sturm-Liouville theory 34M15 Algebraic aspects (differential-algebraic, hypertranscendence, group-theoretical) of ordinary differential equations in the complex domain

Zbl 0077.29201
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