Abstract
A theorem is proved making it possible, in certain cases, to use properties of the series\(\sum\nolimits_k^\infty { = _1 c_k \varphi _k } \) (whereϕ k is an orthonormal system in Hilbert space) to derive properties of the series\(\sum\nolimits_k^\infty { = _1 f(c_k )\varphi } _k \), wheref is a function of a complex variable, holomorphic in a region containing the origin and the points c1, c2,..., ck,..., and such thatf (0)=0.
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M. M. Dei, Normed Linear Spaces [in Russian], Moscow (1961).
I. M. Gel'fand, D. A. Raikov, and G. E. Shilov, Commutative Banach Algebras [in Russian], Moscow (1960).
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Translated from Matematicheskie Zametki, Vol. 8, No. 1, pp. 59–65, July, 1970.
The author wishes to thank G. P. Akilov and S. B. Stechkin for their discussions of the above work.
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Rubinov, A.M. A property of Fourier series. Mathematical Notes of the Academy of Sciences of the USSR 8, 504–507 (1970). https://doi.org/10.1007/BF01093442
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DOI: https://doi.org/10.1007/BF01093442