TY - JOUR

T1 - Interpolation through approximation in a Bernstein space

AU - Shirokov, N. A.

N1 - 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

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

UR - https://link.springer.com/article/10.1007/s10958-019-04597-z

M3 - Article

VL - 243

SP - 965

EP - 980

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -