Geodesic
On the region of values of the system $\{c_2,f(z_1),f(z_2)\}$ in the class of typically real finctions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 24, Tome 371 (2009), pp. 7-17 
E. G. Goluzina. On the region of values of the system $\{c_2,f(z_1),f(z_2)\}$ in the class of typically real finctions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 24, Tome 371 (2009), pp. 7-17. http://geodesic.mathdoc.fr/item/ZNSL_2009_371_a1/
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     author = {E. G. Goluzina},
     title = {On the region of values of the system $\{c_2,f(z_1),f(z_2)\}$ in the class of typically real finctions},
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     year = {2009},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_371_a1/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The author's investigations in the well known class $T$ of typically real functions $f(z)$ in the disk $U=\{z\colon|z|<1\}$ are prolonged. The region of values of the system $\{c_2,f(z_1),f(z_2)\}$ in the class $T$ is investigated. As a corollary, the region of values $f(z_2)$ in the class of functions $f\in T$ with fixed values $c_2$ and $f(z_1)$ is determined. In the proof a criterion of decision power moment problem is used. Bibl. – 8 titles.

[1] E. G. Goluzina, “Ob oblastyakh znachenii nekotorykh sistem funktsionalov v klasse tipichno veschestvennykh funktsii”, Vestn. LGU. Ser. mat., mekh. i astr., 1965, no. 7, 45–62 | MR | Zbl

[2] V. A. Andreeva, N. A. Lebedev, A. V. Stovbun, “Ob oblastyakh znachenii nekotorykh sistem funktsionalov v nekotorykh klassakh regulyarnykh funktsii”, Vestn. LGU. Ser. mat., mekh. i astr., 1961, no. 7, 8–22 | MR | Zbl

[3] Yu. E. Alenitsyn, “Ob oblastyakh izmeneniya sistem koeffitsientov funktsii, predstavimykh summoi integralov Stiltesa”, Vestn. LGU. Ser. mat., mekh. i astr., 1962, no. 7, 25–41 | Zbl

[4] E. G. Goluzina, “O mnozhestve znachenii $f(z_0)$ v odnom klasse tipichno veschestvennykh funktsii”, Zap. nauchn. semin. POMI, 237, 1997, 46–55 | MR | Zbl

[5] M. S. Robertson, “On the coefficients of typically real function”, Bull. Amer. Math. Soc., 41:8 (1935), 565–572 | DOI | MR | Zbl

[6] G. M. Goluzin, “Ob odnom metode variatsii v teorii analiticheskikh funktsii”, Uchen. zap. LGU, 1952, no. 144, 85–101 | MR

[7] M. G. Krein, A. A. Nudelman, Problema momentov Markova i ekstremalnye zadachi, M., 1973

[8] F. R. Gantmakher, Teoriya matrits, 3-e izd., M., 1967