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, Hölder's inequality.
Mots-clés : Fourier multiplier, Laplace transformation 
@article{MZM_2011_89_6_a9,
     author = {A. M. Sedletskii},
     title = {Bases of {Exponentials} in {Weighted} {Spaces} {Generated} by {Zeros} of {Functions} of {Sine} {Type}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {894--913},
     publisher = {mathdoc},
     volume = {89},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_6_a9/}
}
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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/