A characterization of analytic self-maps of the open unit disk in terms of their Taylor coefficients is due to I. Schur. We present a boundary analog of this result.
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Nahum Zobin, Vladimir Bolotnikov, Boundary asymptotic expansions of analytic self-maps of the unit disk. Rev. Mat. Iberoam. 29 (2013), no. 1, pp. 357–371DOI 10.4171/RMI/723