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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 $L_{p}$ ...

On the basis properties of a spectral problem with a spectral parameter in a boundary condition.

Kerimov, N. B.; Mirzoev, V. S. — 2003

Sibirskij Matematicheskij Zhurnal

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

On the basis properties of a spectral problem with a spectral parameter in a boundary condition.

The basis property in $L_{p}$ of the boundary value problem rationally dependent on the eigenparameter