Nonlinear interpolation and norm minimization

We prove that the set of convolution-type functions in _d that satisfy the interpolation conditions contains a unique function whose convolution element has the minimumL_p-norm. The extremal function is determined by solving a nonlinear interpolation problem. The results are applied to an operator recovery problem.Translated fromMatematicheskie Zametki, Vol. 58, No. 4, pp. 512–524, October, 1995.