Abstract
We prove contour-solid theorems for holomorphic functions defined in finely open sets of the complex plane.
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P. M. Tamrazov, “Strengthened contour-solid results for subharmonic functions,” Ukr. Mat. Zh., 40, No. 2, 210–219 (1988).
P. M. Tamrazov, Contour-solid results for holomorphic functions,” Izv. Akad. Nauk SSSR, 50, No. 4, 835–848 (1986).
P. M. Tamrazov and O. A. Sarana, Contour-Solid Properties of Finely Subharmonic Functions [in Russian], Preprint No. 94.33, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1994).
P. M. Tamrazov and O. A. Sarana, “Contour-solid properties of finely hypoharmonic functions,” Ukr. Mat. Zh., 49, No. 8, 114–1125 (1997).
O. A. Sarana, Contour-Solid Theorems for Finely Holomorphic Functions [in Ukrainian], Dep. Ukr. DNTB No. 2346-Uk94, Kiev (1994).
B. Fuglede, “Finely harmonic functions,” Lect. Notes Math., No. 289, Springer, Berlin (1972).
B. Fuglede, “Finely holomorphic functions. A survey,” Rev. Roum. Math. Pures Appl., 33, 283–295 (1988).
B. Fuglede, “Finely harmonic mappings and finely holomorphic functions,” Ann. Acad. Sci. Fenn. Ser. A. I. Math., 2, 113–127 (1976).
B. Fuglede, “Value distribution of harmonic and finely harmonic morphisms and applications in complex analysis,” Ann. Acad. Sci. Fenn. Ser. A. I. Math., 11, 111–136 (1986).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 5, pp. 712–723, May, 1998.
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Tamrazov, P.M., Sarana, A.A. Contour-solid properties of finely holomorphic functions. Ukr Math J 50, 809–821 (1998). https://doi.org/10.1007/BF02514333
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DOI: https://doi.org/10.1007/BF02514333