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

Y. N. Aliyev — 2007

Colloquium Mathematicae

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 L₂(0,1), except for some cases where this system is neither complete nor minimal.

The basis property in L p of the boundary value problem rationally dependent on the eigenparameter

N. B. Kerimov;  Y. N. Aliyev — 2006

Studia Mathematica

We consider a Sturm-Liouville operator with boundary conditions rationally dependent on the eigenparameter. We study the basis property in L p of the system of eigenfunctions corresponding to this operator. We determine the explicit form of the biorthogonal system. Using this we establish a theorem on the minimality of the part of the system of eigenfunctions. For the basisness in L₂ we prove that the system of eigenfunctions is quadratically close to trigonometric systems. For the basisness in L p ...

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