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Expansion of analytic functions in series of rational functions. (English. Russian original) Zbl 0518.30006

Math. Notes 31, 368-375 (1982); translation from Mat. Zametki 31, 723-737 (1982).

MSC:

30B50 Dirichlet series, exponential series and other series in one complex variable
41A58 Series expansions (e.g., Taylor, Lidstone series, but not Fourier series)
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References:

[1] J. Wolf, ?Sur les séries \(\sum\nolimits_{k = 1}^\infty {\frac{{A_k }}{{z - \alpha _k }}} ,\) ? C.R. Acad. Sci.,173, 1327-1328 (1921).
[2] A. Danjoy, ?Sur les séries de fractions rationneles,? Bull. Soc. Math. France,52, 418-434 (1924).
[3] A. A. Gonchar, ?Examples of nonuniqueness of analytic functions,? Vestn. Mosk. Univ., No. 1, 37-43 (1964).
[4] T. A. Leont’eva, ?Representation of functions, analytic in a closed domain, by series of rational functions,? Mat. Zametki,4, No. 2, 191-200 (1968).
[5] L. Brown, A. Shields, and K. Zeller, ?On absolute convergent exponential sums,? Trans. Am. Math. Soc.,96, No. 1, 162-183 (1960). · Zbl 0096.05103 · doi:10.1090/S0002-9947-1960-0142763-8
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