Geodesic
Bases of Exponentials in the Spaces $L^p(-\pi,\pi)$
Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 418-432

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It is proved that systems of exponentials orthogonal to measures of a special kind form bases in $L^p(-\pi,\pi)$, $1$, for which an analog of the Riesz theorem on the projection from $L^p$ onto $H^p$ is valid. 
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     author = {A. M. Sedletskii},
     title = {Bases of {Exponentials} in the {Spaces} $L^p(-\pi,\pi)$},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2002_72_3_a9/}
}
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A. M. Sedletskii. Bases of Exponentials in the Spaces $L^p(-\pi,\pi)$. Matematičeskie zametki, Tome 72 (2002) no. 3, pp. 418-432. http://geodesic.mathdoc.fr/item/MZM_2002_72_3_a9/