Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Two new open mapping theorems for analytic multivalued functions

Authors: Line Baribeau and Sarah Harbottle
Journal: Proc. Amer. Math. Soc. 115 (1992), 1009-1012
MSC: Primary 32E20; Secondary 30G30, 46J15
MathSciNet review: 1086321
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: It is conjectured that the image $ U$ of a domain $ D$, under an analytic multivalued function $ K$, satisfies $ U \cap \partial U \subset { \cap _{\lambda \in D}}K(\lambda )$ if the values of $ K$ are polynomially convex sets. We prove that this conjecture is true in the two special cases when $ K$ is convex-valued and polar-valued.

References [Enhancements On Off] (What's this?)

  • [A] B. Aupetit, Analytic multivalued functions in Banach algebras and uniform algebras, Adv. in Math. 44 (1982), 18-60. MR 654547 (84b:46059)
  • [B-R] B. Berndtsson and T. J. Ransford, Analytic multifunctions, the $ \bar \partial $-equation, and a proof of the corona theorem, Pacific J. Math. 124 (1986), 57-72. MR 850666 (87j:30082)
  • [R1] T. J. Ransford, Open mapping, inversion and implicit function theorems for analytic multivalued functions, Proc. London Math. Soc. (3) 49 (1984), 537-562. MR 759303 (86d:30029)
  • [R2] -, On the range of an analytic multivalued function, Pacific J. Math. 123 (1986), 421-439. MR 840852 (87g:30058)
  • [Sa] A. Sadullaev, Pseudoconcave sets and algebraic lemniscates, preprint.
  • [Sł] Z. Słodkowski, Analytic set-valued functions and spectra, Math. Ann. 256 (1981), 363-386. MR 626955 (83b:46070)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32E20, 30G30, 46J15

Retrieve articles in all journals with MSC: 32E20, 30G30, 46J15

Additional Information

Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society