On the basis property of the root functions of differential operators with matrix coefficients

• Autorzy: Oktay Veliev
• Języki publikacji: EN

Abstrakty

EN

We obtain asymptotic formulas for eigenvalues and eigenfunctions of the operator generated by a system of ordinary differential equations with summable coefficients and periodic or antiperiodic boundary conditions. Then using these asymptotic formulas, we find necessary and sufficient conditions on the coefficients for which the system of eigenfunctions and associated functions of the operator under consideration forms a Riesz basis.

Słowa kluczowe

EN

Differential operators; Eigenfunction expansion

Kategorie tematyczne

• 34L10: Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions
• 47E05: Ordinary differential operators (should also be assigned at least one other classification number in section 47)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 3
• Strony: 657-672

Daty

wydano

2011-06-01

online

2011-03-22

Twórcy

autor

Oktay Veliev

• Dogus University

Bibliografia

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• [16] Veliev O.A., Uniform convergence of the spectral expansion for a differential operator with periodic matrix coefficients, Bound. Value Probl., 2008, ID 628973
• [17] Veliev O.A., On the differential operators with periodic matrix coefficients, Abstr. Appl. Anal., 2009, ID 934905
• [18] Veliev O.A., Shkalikov A.A., On the Riesz basis property of the eigen- and associated functions of periodic and antiperiodic Sturm-Liouville problems, Math. Notes, 2009, 85(5–6), 647–660

Identyfikatory

DOI

10.2478/s11533-011-0015-1