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The completeness of a functional sequence

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Abstract

Let πn(u) be a sequence of polynomials with a biorthogonal system, and let {ℱ n (z)} be functions defined in the singly connected domain D. We consider the problem of the completeness of the system

$$A(z,\lambda _n ) = \sum\nolimits_{s = 0}^\infty {P_\mathfrak{s} } (z)\pi _s (\lambda _n ),n = 1,2,...,$$

in the class of functions F(z) having the representation

$$F(z) = \sum\nolimits_{k = 0}^\infty d _k P_k (z).$$

.

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Authors and Affiliations

  1. Gor'kovsk State University, USSR

    A. A. Mirolyubov

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  1. A. A. Mirolyubov
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Translated from Matematicheskie Zametki, Vol. 12, No. 6, pp. 671–680, December, 1972.

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Mirolyubov, A.A. The completeness of a functional sequence. Mathematical Notes of the Academy of Sciences of the USSR 12, 843–848 (1972). https://doi.org/10.1007/BF01156042

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  • DOI: https://doi.org/10.1007/BF01156042

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