Best approximation in the mean by analytic and harmonic functions

Details Best approximation in the mean by analytic and harmonic functions Best approximation in the mean by analytic and harmonic functions

1999-08-28

arxiv.org/abs/math/9908154v1

Mathematics

Functional Analysis

Plain TeX, 39 pages

Scientific paper

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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