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)

 
 

 

Polynomial hulls with convex sections and interpolating spaces


Author: Zbigniew Slodkowski
Journal: Proc. Amer. Math. Soc. 96 (1986), 255-260
MSC: Primary 32E20; Secondary 46E99, 46M35
DOI: https://doi.org/10.1090/S0002-9939-1986-0818455-X
MathSciNet review: 818455
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Assume that $ L \subset \partial D \times {{\mathbf{C}}^m}$ is compact and has convex vertical sections. Denote by $ K$ its polynomially convex hull. It is shown that $ K\backslash \partial D \times {{\mathbf{C}}^m}$, if nonempty, can be covered by graphs of analytic functions $ f:D \to {{\mathbf{C}}^m}$. The proof is based on complex interpolation theory for families of finite-dimensional normed spaces.


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

  • [1] H. Alexander and J. Wermer, On the approximation of singularity sets by analytic varieties, Pacific J. Math. 104 (1983), 263-268. MR 684289 (84e:32016)
  • [2] -, Polynomial hulls with convex fibers, Math. Ann. 27 (1985), 99-109. MR 779607 (86i:32025)
  • [3] B. Aupetit, Analytic multivalued functions in Banach algebras, Adv. in Math. 44 (1982), 18-60. MR 654547 (84b:46059)
  • [4] R. Coifman, M. Gwikel, R. Rochberg, Y. Sagher and G. Weiss, The complex method for interpolation of operators acting on families of Banach spaces, Lecture Notes in Math., Vol. 779, Springer-Verlag, Berlin and New York, 1980, pp. 123-153. MR 576042 (81k:46075)
  • [5] T. J. Ransford, Analytic multivalued functions, Ph.D. Thesis, University of Cambridge, 1983.
  • [6] Z. Slodkowski, Analytic set-valued functions and spectra, Math. Ann. 256 (1981), 363-386. MR 626955 (83b:46070)
  • [7] -, Analytic multifunctions, $ q$-plurisubharmonic functions and uniform algebras (Proc. Conf. Banach algebras and several complex variables), F. Greenleaf and D. Gulick, editors, Contemp. Math., vol. 32, Amer. Math. Soc., Providence, R. I., 1984, pp. 243-258.
  • [8] -, A generalization of Vesentini and Wermer's theorems. Rend. Sem. Mat. Univ. Padova (to appear).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32E20, 46E99, 46M35

Retrieve articles in all journals with MSC: 32E20, 46E99, 46M35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0818455-X
Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society