Abstract:
With a function $f(z)$, analytic in the unit circle, we associate by a specific rule the series $\sum_{n=1}^\infty\frac{A_n}{a-\lambda_nz}$, $|\lambda_n|<1$. We derive a (necessary and sufficient) condition for the convergence of the series in the unit circle. We derive further conditions under which the series converges to the function $f(z)$ itself.
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