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Journal of Mathematical Sciences

, Volume 243, Issue 6, pp 965–980 | Cite as

Interpolation Through Approximation in a Bernstein Space

  • N. A. ShirokovEmail author
Article
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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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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.St.Petersburg State University and High School of EconomicsSt.PetersburgRussia

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