Geodesic
On the region of values of the system $\{f(z_1),\dots,f(z_n)\}$ in the class of typically real functions. II
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 24-33 
E. G. Goluzina. On the region of values of the system $\{f(z_1),\dots,f(z_n)\}$ in the class of typically real functions. II. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVIII, Tome 323 (2005), pp. 24-33. http://geodesic.mathdoc.fr/item/ZNSL_2005_323_a2/
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     title = {On the region of values of the system $\{f(z_1),\dots,f(z_n)\}$ in the class of typically real {functions.~II}},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The paper studies the region $D_{m,1}(T)$ of values of the system $\{f(z_1),f(z_2),\dots,f(z_m),f(r)\}$, $m\ge1$, where $z_j$ ($j=1,2,\dots,m$) are arbitrary fixed points of the disk $U=\{z:|z|<1\}$ with $\operatorname{Im}z_j\ne0$ ($j=1,2,\ldots,m$), and $r$, $0, is fixed, on the class $T$ of functions $f(z)=z+a_2z^2+\cdots$ regular in the disk $U$ and satisfying in the latter the condition $\operatorname{Im}f(z)\operatorname{Im}z>0$ for $\operatorname{Im}z\ne0$. An algebraic characterization of the set $D_{m,1}(T)$ in terms of nonnegative Hermitian forms is given, and all the boundary functions are described. As an implication, the region of values of $f(z_m)$ in the subclass of functions from the class $T$ with prescribed values $f(z_k)$ ($k=1,2,\dots,m-1$) and $f(r)$ is determined.

[1] E. G. Goluzina, “O mnozhestve znachenii sistemy $\{f(z_1),\dots f(z_n)\}$ v klasse tipichno veschestvennykh funktsii”, Zap. nauchn. semin. POMI, 314, 2004, 41–51 | MR | Zbl

[2] E. G. Goluzina, “O mnozhestve znachenii sistemy $\{f(z_1),f(z_2),f(z_3)\}$ v klasse tipichno veschestvennykh funktsii”, Zap. nauchn. semin. POMI, 302, 2003, 5–17 | MR

[3] E. G. Goluzina, “O mnozhestve znachenii odnoi sistemy funktsionalov v klasse tipichno veschestvennykh funktsii”, Zap. nauchn. semin. POMI, 226, 1996, 69–79

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