We determine the exact values of the upper bounds of the errors of approximation by harmonic splines for functions u defined on an n-dimensional parallelepiped Ω and such that ||Δu|| L∞(Ω) ≤ 1 and functions u defined on Ω and such that ||Δu|| L∞(Ω) ≤ 1, 1 ≤ p ≤ ∞. In the first case, the error is estimated in L p (Ω). 1 ≤ p ≤ ∞. In the second case, the error is estimated in L 1(Ω).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 8, pp. 1011–1024, August, 2012.
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Babenko, V.F., Leskevich, T.Y. Approximation of some classes of functions of many variables by harmonic splines. Ukr Math J 64, 1151–1167 (2013). https://doi.org/10.1007/s11253-013-0706-9
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DOI: https://doi.org/10.1007/s11253-013-0706-9