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Mat. Zametki, 1972, Volume 12, Issue 6, Pages 671–680 (Mi mz9932)  

The completeness of a functional sequence

A. A. Mirolyubov

Gor'kovsk State University

Abstract: Let $\{\pi_n(u)\}$ be a sequence of polynomials with a biorthogonal system, and let $\{\mathscr{P}_n(z)\}$ be functions defined in the singly connected domain $\mathrm{D}$. We consider the problem of the completeness of the system
$$ A(z,\lambda_n)=\sum_{s=0}^\infty\mathscr{P}_s(z)\pi_s(\lambda_n),\qquad n=1,2,…, $$
in the class of functions $\mathrm{F(z)}$ having the representation
$$ F(z)=\sum_{k=0}^\infty d_k \mathscr{P}_k(z). $$


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English version:
Mathematical Notes, 1972, 12:6, 843–848

Bibliographic databases:

UDC: 517.5
Received: 13.10.1970

Citation: A. A. Mirolyubov, “The completeness of a functional sequence”, Mat. Zametki, 12:6 (1972), 671–680; Math. Notes, 12:6 (1972), 843–848

Citation in format AMSBIB
\Bibitem{Mir72}
\by A.~A.~Mirolyubov
\paper The completeness of a functional sequence
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 6
\pages 671--680
\mathnet{http://mi.mathnet.ru/mz9932}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=322148}
\zmath{https://zbmath.org/?q=an:0245.30004}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 6
\pages 843--848
\crossref{https://doi.org/10.1007/BF01156042}


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