Holomorphic functions of slow growth on coverings of pseudoconvex domains in Stein manifolds

Abstract

We apply the methods developed in our previous work to study holomorphic functions of slow growth on coverings of pseudoconvex domains in Stein manifolds. In particular, we extend and strengthen certain results of Gromov, Henkin and Shubin on holomorphic L 2 functions on coverings of pseudoconvex manifolds in the case of coverings of Stein manifolds.

Corona theorem for H∞ on covering of Riemann surfaces of finite type

“…By the hypothesis of the theorem we have |η| := sup z∈U,s∈Sη |g(z, s)| ≤ c||η|| (4.2) for some c depending on U and h Y only. The remaining part of the proof repeats literally the proof of Proposition 5.1 of [Br4]. We refer to this paper for details.…”

On holomorphic functions of slow growth on coverings of strongly pseudoconvex manifolds

“…These and some other results will be published elsewhere. It is worth noting that results much stronger than Theorem 1.1 can be obtained if M is a strongly pseudoconvex Stein manifold, see [2,3] for an exposition.…”

On the approximation property for Banach spaces predual to H∞-spaces

“…The proof uses the techniques developed in [3][4][5]; we refer to these papers for additional details.…”

“…Consider the homomorphism ρ : G → GL (C(B, G)) of G into the group of invertible linear bounded operators on C(B, G) defined by the formula (ρ(g) C(G, B) for all x ∈ U i ∩ U j , see, e.g., [5,Ex. 3.2].…”