Geodesic
Interpolation in a Bernstein space by means of approximation
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 215-237 Cet article a éte moissonné depuis la source Math-Net.Ru

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We denote by $B_\sigma$ the Bernstein space of entire functions of exponential type $\leq\sigma$ bounded on the real axis. Let $\Lambda=\{z_n\}_{n\in\mathbb Z}$, $z_n=x_n+iy_n$, be a sequence such that $x_{n+1}-x_n\geq l>0$ and $|y_n|\leq L$, $n\in\mathbb Z$. We prove that for any sequence $A=\{a_n\}_{n\in~\mathbb Z}$ of bounded $a_n$, $|a_n|\leq M$, $n\in\mathbb Z$, there exists a function $f\in B_\sigma$ with $\sigma\leq\sigma_0(l,L)$ such that $f|_\Lambda=A$. We use a method of approximation by mean of functions from a Bernstein space. 
@article{ZNSL_2018_467_a17,
     author = {N. A. Shirokov},
     title = {Interpolation in {a~Bernstein} space by means of approximation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {215--237},
     year = {2018},
     volume = {467},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a17/}
}
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N. A. Shirokov. Interpolation in a Bernstein space by means of approximation. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 46, Tome 467 (2018), pp. 215-237. http://geodesic.mathdoc.fr/item/ZNSL_2018_467_a17/

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