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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 -<a<b 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=λwy,

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