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Bessel inequality, Riesz theorem and unconditional basis property for root vectors of ordinary differential operators. (Russian) Zbl 0768.34053

Ordinary differential operators of any finite order generated by the differential operator \(lu = u^{(n)} + p_ 1(x)u^{(n-1)}+\dots + p_ n(x)u\), \(x\in G = (0,1)\) are considered. Necessary and sufficient conditions are derived for the systems of the root vectors of the Schrödinger operators to form a Riesz basis. Conditions are found at which the systems of the root vector functions obey the Bessel inequality. An analogue of the Riesz theorem is proved. The results of the work by N. B. Kerimov [Dissertation, Moscow (1985)] are used for the analysis.
Reviewer: V.Burjan (Praha)

MSC:

34L05 General spectral theory of ordinary differential operators
47E05 General theory of ordinary differential operators
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