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On the Riesz basis of a sine system. (Russian) Zbl 0696.34013

Let \(0<x_ 0<1\), \(x_ 0\neq (1-2m+2s)/(1+2m+2s)\) for \(m=1,2,...\), \(s=0,1,2,... \). The author proves that the eigenfunction system \(\{\sin \pi kx/(1+(-1)^{k+1}x_ 0)\}^{\infty}_{k=1}\) of the nonlocal boundary value problem \(u''+\lambda u=0\), \(u(0)=0\), \(u(1)=u(x_ 0)\) is a Riesz basis in \(L^ 2[0,1]\).
Reviewer: N.Bozhinov

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
42C30 Completeness of sets of functions in nontrigonometric harmonic analysis
42C15 General harmonic expansions, frames
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