Vol. 46, No. 2, 1973

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Boundedly holomorphic convex domains

Dong S. Kim

Vol. 46 (1973), No. 2, 441–449

A boundedly holomorphic convex domain is a holomorphically convex domain with respect to the algebra of bounded holomorphic functions in the domain. The followings are shown in this paper: In a Riemann domain, a boundedly holomorphic convex domain is a domain of bounded holomorphy. With some restrictions, the converse is true. The spectrum of the algebra B of bounded holomorphic functions is an envelope of bounded holomorphy provided that the completion of B with the topology of uniform convergence on compact subsets is stable under differentiation. Finally, Stein manifolds of bounded type are introduced.

Mathematical Subject Classification 2000
Primary: 32D15
Received: 14 December 1971
Revised: 7 July 1972
Published: 1 June 1973
Dong S. Kim