Best approximation in the mean by analytic and harmonic functions
Dmitry Khavinson, John E. McCarthy, Harold S. Shapiro
Abstract
We consider the problem of finding the best harmonic or analytic approximant to a given function. We discuss when the best approximant is unique, and what regularity properties the best approximant inherits from the original function. All our approximations are done in the mean with respect to Lebesgue measure in the plane or higher dimensions.
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