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Zbl 1228.34045
Qi, Jiangang; Zheng, Zhaowen; Sun, Huaqing
Classification of Sturm-Liouville differential equations with complex coefficients and operator realizations. (English)
[J] Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 467, No. 2131, 1835-1850 (2011). ISSN 1364-5021; ISSN 1471-2946/e

Summary: In this paper, a new classification of Sturm-Liouville differential equations with complex coefficients is given. Compared with the corresponding result of {\it B. M. Brown} et al. [ibid. 455, No. 1984, 1235--1257 (1999; Zbl 0944.34018); Proc. Lond. Math. Soc., III. Ser. 87, No. 2, 419--450 (2003; Zbl 1055.34048)], this classification reveals the great effects of rotation angle and it is independent of the rotation angles. Moreover, the asymptotic behaviours of functions in the maximal domain are presented and J-self-adjoint extensions associated with the differential equations are characterized.

MSC 2000:: *34B20 Weyl theory and its generalizations
34B24 Sturm-Liouville theory
34L15 Estimation of eigenvalues for OD operators
47E05 Ordinary differential operators

Keywords: Sturm-Liouville differential equation; non-self-adjoint; limit-point (circle) case; J-self-adjoint extension

Citations: Zbl 0944.34018; Zbl 1055.34048

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Zentralblatt MATH Berlin [Germany]