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 Computation of Hankel matrices in terms of classical kernel functions in potential theory J. Korean Math. Soc.Published online January 9, 2020 Young-Bok Chung Chonnam National University Abstract : In this paper, we compute the Hankel matrix representation of the Hankel operator on the Hardy space of a general bounded domain with respect to special orthonormal bases for the Hardy space and its orthogonal complement. Moreover we obtain the compact form of the Hankel matrix for the unit disc case with respect to these bases. One can see that the Hankel matrix generated by this computation turns out to be a generalization of the case of the unit disc from the single simply connected domain to multiply connected domains with much diversities of bases. Keywords : Henkel operator, Hankel matrix, Hardy space MSC numbers : 47B35, 30C40 Full-Text :