Geodesic
Bases of Exponentials in Weighted Spaces Generated by Zeros of Functions of Sine Type
Matematičeskie zametki, Tome 89 (2011) no. 6, pp. 894-913

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If $\omega$ is an $A_p$-weight with some additional condition and $(\lambda)$ is a separated sequence of all zeros of a sine-type function possessing a certain multiplier (in the sense of Fourier transforms) property, then the corresponding system of exponentials $(e^{i\lambda_nt})$ constitutes a basis in the weighted space $L^p((-\pi,\pi),\omega(t)\,dt)$, $1<\pi<\infty$.
Keywords: basis of exponentials, weighted space, sine-type function, $A_p$-weight, Riesz property, weighted multiplier
Mots-clés : Fourier multiplier, Laplace transformation, Hölder's inequality. 
A. M. Sedletskii. Bases of Exponentials in Weighted Spaces Generated by Zeros of Functions of Sine Type. Matematičeskie zametki, Tome 89 (2011) no. 6, pp. 894-913. http://geodesic.mathdoc.fr/item/MZM_2011_89_6_a9/
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