Abstract
We announce the resolution of a number of outstanding questions regarding real and complex Chebyshev (supremum norm) approximation by rational functions on a disk and on an interval. The proofs consist mainly of symmetry arguments applied to explicit examples. The most important results: complex rational best approximations on a disk are in general not unique; real functions on an interval can in general be approximated arbitrarily much better by complex rational functions than by real ones. Details will appear in [3, 8].
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