Abstract
With a functionf(z), analytic in the unit circle, we associate by a specific rule the series\(\sum\nolimits_{n = 1}^\infty {\frac{{A_n }}{{1 - \lambda _n z}},\left| {\lambda _n } \right|< 1} \). 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 functionf(z) itself.
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T. A. Leont'eva, “On the representation of functions in the unit circle by rational fraction series,” Matem. Sb., 84(126), No. 2, 313–326 (1971).
T. A. Leont'eva, “Representation of analytic functions by series of rational functions,” Matem. Zametki,2, No. 4, 347–356 (1967).
T. A. Leont'eva, “Representation of functions analytic in a closed region by series of rational functions,” Matem. Zametki,4, No. 2, 191–200 (1968).
A. A. Gonchar, “On the quasianalytic continuation of analytic functions through a Jordan arc,” Dokl. Akad. Nauk SSSR, 166, No. 5, 1028–1031 (1966).
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Translated from Matematicheskie Zametki, Vol. 15, No. 2, pp. 197–203, February, 1974.
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Leont'eva, T.A. Conditions for the representability of analytic functions by series of rational functions. Mathematical Notes of the Academy of Sciences of the USSR 15, 112–115 (1974). https://doi.org/10.1007/BF02102389
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DOI: https://doi.org/10.1007/BF02102389