Bliznyuk, S. V. Optimal recovery of the values of a harmonic function from its Fourier coefficients. (Russian) Zbl 1100.31001 Vladikavkaz. Mat. Zh. 6, No. 4, 10-16 (2004). Given \(2n+1\) Fourier coefficients of the boundary value of a harmonic function \(f\) defined on the unit circle and a point \((x,y)\) in this circle, the optimal recovery problem for the value \(f(x,y)\) is studied. A computational scheme is proposed for an arbitrary \(n\), while the accuracy of the optimal recovery and the optimal computational scheme are found for \(n\leq 4\). Reviewer: Victor Alexandrov (Novosibirsk) MSC: 31A05 Harmonic, subharmonic, superharmonic functions in two dimensions 42A10 Trigonometric approximation 65D15 Algorithms for approximation of functions 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series Keywords:Poisson kernel; Lagrange principle; trigonometric polynomial × Cite Format Result Cite Review PDF Full Text: EMIS