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holomorphic function; reflected Cauchy’s operator; reflected double layer potential
Necessary and sufficient conditions are given for the reflected Cauchy's operator (the reflected double layer potential operator) to be continuous as an operator from the space of all continuous functions on the boundary of the investigated domain to the space of all holomorphic functions on this domain (to the space of all harmonic functions on this domain) equipped with the topology of locally uniform convergence.
[1] E. Dontová M. Dont J. Král: Reflection and a mixed boundary value problem concerning analytic functions. Math. Bohem. 122 (1997), 317-336. MR 1600664
[2] H. Federer: Geometric Measure Theory. Springer-Vєrlag, Berlin, 1969. MR 0257325 | Zbl 0176.00801
[3] J. Král: Integral Operators in Potential Theory. Lecture Notes in Mathematics 823, Springer-Verlag, Berlin, 1980. MR 0590244
[4] S. Saks: Theory of the Integral. Dover Publications, New York, 1964. MR 0167578
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