Optimal recovery of a harmonic function from inaccurate information on the values of the radial integration operator

Bagramyan T.
Vladikavkaz Mathematical Journal 2012. Vol. 14. Issue 1.

Abstract:
We consider the problem of optimal recovery of a harmonic function in the unit ball from the inaccurate values of the radial integration operator. Information on the values of the operator is given as a function that differs from the exact values in the mean-square metric not more than a fixed error, either in the form of a finite set of Fourier coefficients calculated with a fixed error in the mean square or uniform metric.

Keywords: optimal recovery, harmonic function, computerized tomography

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