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Iceberg‐type problems: Estimating Hidden parts of a continuum from the visible parts

Iceberg‐type problems: Estimating Hidden parts of a continuum from the visible parts

Abstract We consider the complex plane \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {C}$\end{document} as a space filled by two different media, separated by the real axis \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {R}$\end{document} . We define \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {H}_+=\lbrace z: \,\Im \,z>0\rbrace$\end{document} to be the upper half‐plane. For a planar body E in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {C}$\end{document} , we discuss a problem of …