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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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/

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