An open mapping theorem for analytic multifunctions

• Autorzy: Zbigniew Słodkowski
• Języki publikacji: EN

Abstrakty

EN

The paper gives sufficient conditions for projections of certain pseudoconcave sets to be open. More specifically, it is shown that the range of an analytic set-valued function whose values are simply connected planar continua is open, provided there does not exist a point which belongs to boundaries of all the fibers. The main tool is a theorem on existence of analytic discs in certain polynomially convex hulls, obtained earlier by the author.

Kategorie tematyczne

• 32E20: Polynomial convexity
• 32Txx: Pseudoconvex domains

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 122
• Numer: 2
• Strony: 117-122

Daty

wydano

1997

otrzymano

1995-04-24

poprawiono

1996-06-03

Twórcy

autor

Zbigniew Słodkowski

• Department of Mathematics, Statistics and Computer Science, College of Liberal Arts and Sciences, University of Illinois at Chicago, 851 South Morgan Str. Chicago, Illinois 60607-7045, U.S.A.

Bibliografia

• [BaHa] L. Baribeau and S. Harbottle, Two new open mapping theorems for analytic multifunctions, Proc. Amer. Math. Soc. 115 (1992), 1009-1012.
• [Ok] K. Oka, Note sur les familles de fonctions analytiques multiformes etc., J. Sci. Hiroshima Univ. 4 (1934), 93-98.
• [Ra1] T. J. Ransford, Open mapping, inversion and implicit function theorems for analytic multivalued functions, Proc. London Math. Soc. 49 (1984), 537-562.
• [Ra2] T. J. Ransford, On the range of an analytic multivalued function, Pacific J. Math. 123 (1986), 421-439.
• [Sł1] Z. Słodkowski, Analytic set-valued functions and spectra, Math. Ann. 256 (1981), 363-386.
• [Sł2] Z. Słodkowski, Polynomial hulls in $ℂ^2$ and quasi-circles, Ann. Scuola Norm. Sup. Pisa (4) 16 (1989), 367-391.