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

• Autorzy: N. B. Kerimov , Y. N. Aliyev
• Języki publikacji: EN

Abstrakty

EN

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 $L_{p}$ we use F. Riesz's theorem.

Kategorie tematyczne

• 34L10: Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions
• 34L20: Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions
• 34B24: Sturm-Liouville theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 174
• Numer: 2
• Strony: 201-212

Daty

wydano

2006

Twórcy

autor

N. B. Kerimov

• Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan, F. Agayev St. 9, Baku AZ 1141, Azerbaijan

autor

Y. N. Aliyev

• Department of Mathematics, Faculty of Pedagogics, Qafqaz University, Khyrdalan, Baku AZ 0101, Azerbaijan

Identyfikatory

DOI

10.4064/sm174-2-6