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On a basic problem for a second order differential equation with a discontinuous coefficient and a spectral parameter in the boundary conditions. (English) Zbl 1109.34061
Mladenov, Ivaïlo (ed.) et al., Proceedings of the 7th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 2--10, 2005. Sofia: Bulgarian Academy of Sciences (ISBN 954-8495-30-9/pbk). 218-225 (2006).
The author considers a Sturm-Liouville problem on a finite interval $[a,b]$ with parameter dependent boundary conditions and an interface condition. The coefficients are such that the problem has a selfadjoint realization in the space $L_2[a,b]\oplus \Bbb C^n$ for $n=2$ or $n=3$ with a definite and indefinite inner product. Then, the standard theory of selfadjoint operators with compact resolvent in Hilbert and Krein spaces, respectively, leads to results on (Riesz) basis property of the eigenvectors (and associated vectors). For the entire collection see [Zbl 1089.53004].
##### MSC:
 34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions (ODE) 34B24 Sturm-Liouville theory 34B10 Nonlocal and multipoint boundary value problems for ODE 34B09 Boundary eigenvalue problems for ODE