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Necessary and sufficient conditions for the Riesz basis property of the eigen- and associated functions of high-order differential operators on an interval. (English. Russian original) Zbl 1155.47047

Dokl. Math. 77, No. 2, 290-292 (2008); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 419, No. 5, 601-603 (2008).
The author considers formally non-selfadjoint differential operator
\[ Lu=u^{(n)}(x)+p_{1}(x)u^{(n-1)}(x)+\cdots +p_{n}(x)u(x),\quad n\geq 2, \]
on an arbitrary finite interval \(G\) of the real line. Necessary and sufficient conditions for the Riesz basis property of systems of eigen- and associated functions of \(L\) are established in terms of the Fourier coefficients and the norms of system elements in other spaces.

MSC:

47E05 General theory of ordinary differential operators
34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators
34L05 General spectral theory of ordinary differential operators
47A75 Eigenvalue problems for linear operators
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References:

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