Let Bσ be the Bernstein space of entire functions of exponential type at most σ bounded on the real axis. Consider a sequence Λ = {zn}n∈ℤ, zn = xn + iyn, such that xn+1 − xn ≥ l > 0 and |yn| ≤ L, n ∈ ℤ. Using approximation by functions from Bσ, we prove that for any bounded sequence A = {an}n∈ℤ, |an| ≤ M, n ∈ ℤ, there exists a function f ∈ Bσ with σ ≤ σ0(l,L) such that f|Λ = A.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 467, 2018, pp. 215–237.
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Shirokov, N.A. Interpolation Through Approximation in a Bernstein Space. J Math Sci 243, 965–980 (2019). https://doi.org/10.1007/s10958-019-04597-z
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DOI: https://doi.org/10.1007/s10958-019-04597-z