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On the basis property of the root functions of differential operators with matrix coefficients. (English) Zbl 1245.34083

The author proves a number of theorems on the Riesz basis property of the root functions of the Sturm-Liouville operator \(H\). Asymptotic formulas for the eigenvalues and eigenfunctions of the operator \(L\) are obtained. The operator is generated by a system of ordinary differential equations with summable coefficients and periodic and antiperiodic boundary conditions. Necessary and sufficient conditions on the coefficients \(P_2(x)\) for which the root functions of \(L\) form a Riesz basis are then determined.

MSC:

34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
47E05 General theory of ordinary differential operators
34L15 Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
34L20 Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators
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References:

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