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On the basis property of a trigonometric system of functions. (Russian) Zbl 0602.42033

The paper deals with the trigonometric system sin(n-\(\beta\) /2), \(n=1,2,..\). where \(\beta =\beta_ 1+i\beta_ 2\) is a complex parameter. The basis theorem state that this system is a basics of \(L_ p[0,\pi]\), \(1<p<\infty\) iff \(-1/p<\beta_ 1<2-1/p\). The coefficients \(B_ n\) in the biorthogonal expansion \(\psi (\theta)=\sum^{\infty}_{n=1}B_ n\sin (n-\beta /2)\) of an arbitrary function \(\psi \in L_ p[0,\pi]\) are found as well.
Reviewer: N.Bozhinov

MSC:

42C30 Completeness of sets of functions in nontrigonometric harmonic analysis
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