Browse > Article
http://dx.doi.org/10.4134/JKMS.j190635

APPROXIMATION BY HOLOMORPHIC FUNCTIONS OF SEVERAL COMPLEX VARIABLES  

Krantz, Steven G. (Department of Mathematics Washington University in St. Louis)
Min, Baili (Department of Mathematics Huazhong University of Science and Technology)
Publication Information
Journal of the Korean Mathematical Society / v.57, no.5, 2020 , pp. 1287-1298 More about this Journal
Abstract
Inspired by a classical approximation result of Bagemihl and Seidel on the disc, we provide generalized results on some proper domains in ℂn about approximation of a continuous function by a holomorphic function in the Mergelyan's style.
Keywords
Several complex variables; Mergelyan approximation; starshaped; starlike mapping;
Citations & Related Records
연도 인용수 순위
  • Reference
1 F. Bagemihl and W. Seidel, Some boundary properties of analytic functions, Math. Z. 61 (1954), 186-199. https://doi.org/10.1007/BF01181342   DOI
2 Ph. Charpentier, Y. Dupain, and M. Mounkaila, Approximation par des fonctions holomorphes a croissance controlee, Publ. Mat. 38 (1994), no. 2, 269-298. https://doi.org/10.5565/PUBLMAT_38294_02   DOI
3 J. Garnett, On a theorem of Mergelyan, Pacific J. Math. 26 (1968), 461-467. http://projecteuclid.org/euclid.pjm/1102985735   DOI
4 S. Gong, Convex and starlike mappings in several complex variables, Mathematics and its Applications (China Series), 435, Kluwer Academic Publishers, Dordrecht, 1998. https://doi.org/10.1007/978-94-011-5206-8
5 M. Hakim and N. Sibony, Boundary properties of holomorphic functions in the ball of $C^n$, Math. Ann. 276 (1987), no. 4, 549-555. https://doi.org/10.1007/BF01456984   DOI
6 K. Kikuchi, Starlike and convex mappings in several complex variables, Pacific J. Math. 44 (1973), 569-580. http://projecteuclid.org/euclid.pjm/1102947954   DOI
7 S. G. Krantz, Function Theory of Several Complex Variables, reprint of the 1992 edition, AMS Chelsea Publishing, Providence, RI, 2001. https://doi.org/10.1090/chel/340
8 N. Levenberg, Approximation in CN, Surv. Approx. Theory 2 (2006), 92-140.
9 S. N. Mergelyan, Uniform approximations of functions of a complex variable, Uspehi Matem. Nauk (N.S.) 7 (1952), no. 2(48), 31-122.
10 W. Rudin, Function Theory in the Unit Ball of $C^n$, reprint of the 1980 edition, Classics in Mathematics, Springer-Verlag, Berlin, 2008.