Geodesic
Minimality of the system of root functions of Sturm–Liouville problems with decreasing affine boundary conditions
Y. N. Aliyev1
1 Department of Mathematics Faculty of Pedagogy Qafqaz University, Khyrdalan Baku AZ 0101, Azerbaijan and Department of Mathematical Analysis Faculty of Mechanics-Mathematics Baku State University Z. Khalilov street 23 Baku AZ 1148, Azerbaijan
Colloquium Mathematicum, Tome 109 (2007) no. 1, pp. 147-162.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm109-1-12
Keywords: consider sturm liouville problems boundary condition linearly dependent eigenparameter study decreasing dependence where non real multiple eigenvalues possible determining explicit form biorthogonal system prove system root eigen associated functions arbitrary element removed minimal system except cases where system neither complete nor minimal

Y. N. Aliyev 1

1 Department of Mathematics Faculty of Pedagogy Qafqaz University, Khyrdalan Baku AZ 0101, Azerbaijan and Department of Mathematical Analysis Faculty of Mechanics-Mathematics Baku State University Z. Khalilov street 23 Baku AZ 1148, Azerbaijan 
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Y. N. Aliyev. Minimality of the system of root functions
 of Sturm–Liouville problems with decreasing
 affine boundary conditions. Colloquium Mathematicum, Tome 109 (2007) no. 1, pp. 147-162. doi : 10.4064/cm109-1-12. http://geodesic.mathdoc.fr/articles/10.4064/cm109-1-12/

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