Vol. 26, No. 2, 1968

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The second Cousin problem with bounded data

Edgar Lee Stout

Vol. 26 (1968), No. 2, 379–387

Given a complex manifold M, an open covering 𝒱 ≡{V α}αA, and, for each α A a function fα holomorphic on V α such that for all α, α′∈ A, fαfα1 is a zero-free holomorphic function on V α V α, the associated second Cousin problem is the problem of showing the existence of a function F holomorphic on M such that for all α, Ffα1 is a zero free function holomorphic on V α. In the present paper we consider an analogous problem in the case that M is the open unit polycylinder UN = {(z1,,zN) CN : |z1| < 1,,|zN| < 1}, that the functions fα are required to be bounded and that the sought function F is also required to be bounded.

Mathematical Subject Classification
Primary: 32.20
Received: 6 April 1967
Published: 1 August 1968
Edgar Lee Stout