Abstract
A different approach to the problem of uniform approximations by the module of bi-analytic functions is outlined. This note follows the ideas from Khavinson (On a geometric approach to problems concerning Cauchy integrals and rational approximation. PhD thesis, Brown University, Providence, RI (1983), Proc Am Math Soc 101(3):475–483 (1987), Michigan Math J 34(3):465–473 (1987), Contributions to operator theory and its applications (Mesa, AZ, 1987). Birkhauser, Basel (1988)), Gamelin and Khavinson (Am Math Mon 96(1):18–30 (1989)) and the more recent paper (Abanov et al. A free boundary problem associated with the isoperimetric inequality. arXiv:1601.03885, 2016 preprint), regarding approximation of \(\overline {z}\) by analytic functions.
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