Geodesic
Necessary and sufficient conditions for extending a function to a Carathéodory function
Sbornik. Mathematics, Tome 213 (2022) no. 11, pp. 1488-1506 Cet article a éte moissonné depuis la source Math-Net.Ru

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A criterion deciding whether a function given by its values (with multiplicities) at a sequence of points in the disc $\mathbb D=\{|z|<1\}$ can be extended to a holomorphic function with nonnegative real part in $\mathbb D$ is stated and proved. In the case when this function is given by the values of its derivatives at $z=0$, this is the well-known Carathéodory criterion. It is also shown that Carathéodory's criterion is a consequence of Schur's criterion and, conversely, Schur's criterion follows from Carathéodory's. Bibliography: 10 titles.
Keywords: continued fractions, Schur's algorithm, Hankel determinants.
Mots-clés : Carathéodory function 
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V. I. Buslaev. Necessary and sufficient conditions for extending a function to a Carathéodory function. Sbornik. Mathematics, Tome 213 (2022) no. 11, pp. 1488-1506. http://geodesic.mathdoc.fr/item/SM_2022_213_11_a1/

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