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Optimal recovery of the values of a harmonic function from its Fourier coefficients. (Russian) Zbl 1100.31001

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 \(n\leq 4\).

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