Minimality of the system of root functions of Sturm–Liouville problems with decreasing affine boundary conditions

Volume 109 / 2007

Y. N. Aliyev Colloquium Mathematicum 109 (2007), 147-162 MSC: 34B24, 34L10. DOI: 10.4064/cm109-1-12


We consider Sturm–Liouville problems with a boundary condition linearly dependent on the eigenparameter. We study the case of decreasing dependence where non-real and multiple eigenvalues are possible. By determining the explicit form of a biorthogonal system, we prove that the system of root (i.e. eigen and associated) functions, with an arbitrary element removed, is a minimal system in $L_2(0,1)$, except for some cases where this system is neither complete nor minimal.


  • Y. N. AliyevDepartment of Mathematics
    Faculty of Pedagogy
    Qafqaz University, Khyrdalan
    Baku AZ 0101, Azerbaijan
    Department of Mathematical Analysis
    Faculty of Mechanics-Mathematics
    Baku State University
    Z. Khalilov street 23
    Baku AZ 1148, Azerbaijan

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