Abstract
We study \(L^2\) approximations of rational functions on the complex plane, focusing on bounded point derivations. We show that if there is a bounded point derivation at x and \(\{x_n\}\) is a sequence of points that converges non-tangentially to x, then the sequence of derivatives \(\{f^{\prime }(x_n)\}\) is uniformly bounded for a large class of functions, specifically those functions which can be approximated by rational functions with poles off X in the \(L^2\) norm. A counterexample is constructed that shows that the hypothesis of non-tangential convergence cannot be removed.
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Communicated by Vladimir Bolotnikov.
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Deterding, S. Non-tangential Limits and Bounded Point Derivations on \(R^2(X)\). Complex Anal. Oper. Theory 18, 39 (2024). https://doi.org/10.1007/s11785-024-01486-5
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DOI: https://doi.org/10.1007/s11785-024-01486-5