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

MathSciNet review:
818455

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Assume that is compact and has convex vertical sections. Denote by its polynomially convex hull. It is shown that , if nonempty, can be covered by graphs of analytic functions . The proof is based on complex interpolation theory for families of finite-dimensional normed spaces.

**[1]**Herbert Alexander and John Wermer,*On the approximation of singularity sets by analytic varieties*, Pacific J. Math.**104**(1983), no. 2, 263–268. MR**684289****[2]**Herbert Alexander and John Wermer,*Polynomial hulls with convex fibers*, Math. Ann.**271**(1985), no. 1, 99–109. MR**779607**, 10.1007/BF01455798**[3]**Bernard Aupetit,*Analytic multivalued functions in Banach algebras and uniform algebras*, Adv. in Math.**44**(1982), no. 1, 18–60. MR**654547**, 10.1016/0001-8708(82)90064-0**[4]**R. R. Coifman, R. Rochberg, G. Weiss, M. Cwikel, and Y. Sagher,*The complex method for interpolation of operators acting on families of Banach spaces*, Euclidean harmonic analysis (Proc. Sem., Univ. Maryland, College Park, Md., 1979) Lecture Notes in Math., vol. 779, Springer, Berlin, 1980, pp. 123–153. MR**576042****[5]**T. J. Ransford,*Analytic multivalued functions*, Ph.D. Thesis, University of Cambridge, 1983.**[6]**Zbigniew Słodkowski,*Analytic set-valued functions and spectra*, Math. Ann.**256**(1981), no. 3, 363–386. MR**626955**, 10.1007/BF01679703**[7]**-,*Analytic multifunctions*,*-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).

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