Abstract
We prove some local contour-solid theorems for finely holomorphic functions defined on sets of the complex plane that are finely open with nonpolar complements.
Similar content being viewed by others
REFERENCES
P. M. Tamrazov and A. A. Sarana, “Contour-solid properties of finely hypoharmonic functions,” Ukr. Mat. Zh., 49, No. 8, 1114–1125 (1997).
P. M. Tamrazov and A. A. Sarana, “Contour-solid properties of finely holomorphic functions,” Ukr. Mat. Zh., 50, No. 5, 712–723 (1998).
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).
T. G. Aliev and P. M. Tamrazov, Meromorphic Functions in Contour-Solid Problem with Regard to Zeros and Multivalence [in Russian], Preprint No. 85.46, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1985).
B. Fuglede, “Finely harmonic functions,” Lect. Notes Math., No. 289, Springer, Berlin (1972).
B. Fuglede, “Sur la fonction de Green pour un domaine fin,” Ann. Inst. Fourier., 25, No. 3–4, 201–206 (1975).
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).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sarana, A.A. Some Local Contour-Solid Theorems for Finely Holomorphic Functions. Ukrainian Mathematical Journal 54, 2038–2046 (2002). https://doi.org/10.1023/A:1024081500428
Issue Date:
DOI: https://doi.org/10.1023/A:1024081500428