On Complex Valued Functions with Strongly Unique Best Chebyshev Approximation Original Research Article

In contrast to the complex case, the best Chebyshev approximation with respect to a finite-dimensional Haar subspace V ⊂ C(Q) (Q compact) is always strongly unique if all functions are real valued. However, strong uniqueness still holds for complex valued functions ƒ with a so-called reference of maximal length. It is known that this class forms an open and dense subset in C(Q) if the number of isolated points of Q does not exceed dim V. In this paper, we show that this result also holds in the space A(Q) of functions, analytic in the interior of Q, if Q satisfies a certain regularity condition.