This article is cited in 2 papers

Constrained extremal problems in $H^2$ and Carleman's formulae

L. Baratchart, J. Leblond, F. Seyfert

Institut National de Recherche en Informatique et en Automatique, Sophia Antipolis – Méditerranée, France

Abstract: We consider the extremal problem of best approximation to some function $f$ in $L^2(I)$, with $I$ a subset of the circle, by the trace of a Hardy function whose modulus is bounded pointwise by some gauge function on the complementary subset.
Bibliography: 36 titles.

Keywords: Hardy spaces, extremal problems, approximations in the complex domain, Cauchy problem, inverse boundary problems.

UDC: 517.538.5

MSC: Primary 41A50; Secondary 30D55, 30E10, 35R25

Received: 30.12.2016 and 09.02.2018

DOI: 10.4213/sm8900

 English version: Sbornik: Mathematics, 2018, 209:7, 922–957

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