Geodesic
Representation of functions in the unit disk by series of rational fractions
Sbornik. Mathematics, Tome 13 (1971) no. 2, pp. 309-322 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is shown that if $f(z)=\sum_{n=0}^\infty a_nz^n$, $a_n=O(1/n^p)$, $p>1$, then $f(z)$ can be expanded in a series $$ f(z)=\sum_{k=1}^\infty\frac{A_k}{1-\lambda_kz},\qquad|\lambda_k|<1, $$ that converges uniformly inside the unit disk $|z|<1$. For $p>2$ the expansion is valid in the closed disk $|z|\leqslant1$, and $\sum_{k=1}^\infty|A_k|<\infty$. Bibliography: 6 titles. 
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     title = {Representation of functions in the unit disk by series of rational fractions},
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T. A. Leont'eva. Representation of functions in the unit disk by series of rational fractions. Sbornik. Mathematics, Tome 13 (1971) no. 2, pp. 309-322. http://geodesic.mathdoc.fr/item/SM_1971_13_2_a7/

[1] I. Wolff, “Sur les séries $\sum\limits_{k=1}^\infty\dfrac{A_k}{z-a_k}$”, C. R. Acad. Sci., 173 (1921), 1327–1328 | Zbl

[2] Dzh. L. Uolsh, Interpolyatsiya i approksimatsiya ratsionalnymi funktsiyami v kompleksnoi oblasti, IL, Moskva, 1961 | MR

[3] A. Denjoy, “Sur les series des fractions rationnelles”, Bull. Soc. Math. France, 52 (1924), 418–434 | MR

[4] T. A. Leonteva, “Predstavlenie funktsii, analiticheskikh v zamknutoi oblasti, ryadami ratsionalnykh funktsii”, Matem. zametki, 4:2 (1968), 191–200 | MR

[5] A. A. Gonchar, “O kvazianaliticheskom prodolzhenii analiticheskikh funktsii cherez zhordanovu dugu”, DAN SSSR, 166:5 (1966), 1028–1031 | Zbl

[6] T. A. Leonteva, “Predstavlenie analiticheskikh funktsii ryadami ratsionalnykh funktsii”, Matem. zametki, 2:4 (1967), 347–356 | MR | Zbl