On the Basis Property of the Root Functions of Differential Operators with Matrix Coefficients

2009/12/22 by O. A. Veliev, Veliev, O. A.
Computer Science · Mathematics · #34A25 #47E05 #Differential Equations and Boundary Problems #FOS: Mathematics #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0912.4340

openalex publication_date 2009/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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