Geodesic
A property of Fourier series
Matematičeskie zametki, Tome 8 (1970) no. 1, pp. 59-65

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A theorem is proved making it possible, in certain cases, to use properties of the series $\sum_{k=1}^\infty c_k\varphi_k$ (where $\{\varphi_k\}$ is an orthonormal system in Hilbert space) to derive properties of the series $\sum_{k=1}^\infty f(c_k)\varphi_k$, where $f$ is a function of a complex variable, holomorphic in a region containing the origin and the points $c_1, c_2, \dots, c_k, \dots$, and such that $f (0)=0$. 
@article{MZM_1970_8_1_a6,
     author = {A. M. Rubinov},
     title = {A property of {Fourier} series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {59--65},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_1_a6/}
}
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A. M. Rubinov. A property of Fourier series. Matematičeskie zametki, Tome 8 (1970) no. 1, pp. 59-65. http://geodesic.mathdoc.fr/item/MZM_1970_8_1_a6/