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
$$
A(z,\lambda_n)=\sum_{s=0}^\infty\mathscr{P}_s(z)\pi_s(\lambda_n),\qquad n=1,2,\dots,
$$
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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