Chung, Young-Bok Computation of Hankel matrices in terms of classical kernel functions in potential theory. (English) Zbl 07240933 J. Korean Math. Soc. 57, No. 4, 973-986 (2020). Summary: : 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. MSC: 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators 30C40 Kernel functions in one complex variable and applications Keywords:Hankel operator; Hankel matrix; Hardy space PDFBibTeX XMLCite \textit{Y.-B. Chung}, J. Korean Math. Soc. 57, No. 4, 973--986 (2020; Zbl 07240933) Full Text: DOI References: [1] S. Bell,Solving the Dirichlet problem in the plane by means of the Cauchy integral, Indiana Univ. Math. J.39(1990), no. 4, 1355-1371.https://doi.org/10.1512/iumj. 1990.39.39060 · Zbl 0797.31003 [2] ,The Szeg˝o projection and the classical objects of potential theory in the plane, Duke Math. J.64(1991), no. 1, 1-26.https://doi.org/10.1215/S0012-7094-91-06401X · Zbl 0739.31002 [3] ,The Cauchy transform, potential theory, and conformal mapping, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992. [4] A. Brown and P. R. Halmos,Algebraic properties of Toeplitz operators, J. Reine Angew. Math.213(1963/64), 89-102.https://doi.org/10.1007/978-1-4613-8208-9_19 · Zbl 0116.32501 [5] Y.-B. Chung,Classification of Toeplitz operators on Hardy spaces of bounded domains in the plane, Math. Notes101(2017), no. 3-4, 529-541.https://doi.org/10.1134/ S0001434617030142 · Zbl 1443.47031 [6] P. R. Garabedian,Schwarz’s lemma and the Szeg¨o kernel function, Trans. Amer. Math. Soc.67(1949), 1-35.https://doi.org/10.2307/1990414 · Zbl 0035.05402 [7] K. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.