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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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IMPACT FACTOR 2016: 0.755
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1435-5337
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Volume 20, Issue 5 (Jan 2008)

Issues

Approximation of holomorphic mappings on strongly pseudoconvex domains

Barbara Drinovec-Drnovšek
  • Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia.
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Franc Forstnerič
  • Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia.
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2008-11-03 | DOI: https://doi.org/10.1515/FORUM.2008.039

Abstract

Let D be a relatively compact strongly pseudoconvex domain in a Stein manifold S. We prove that for every complex manifold Y the set 𝒜(D, Y) of all continuous maps Y which are holomorphic in D is a complex Banach manifold, and every ƒ ∈ 𝒜(D, Y) can be approximated uniformly on by maps holomorphic in open neighborhoods of in S. Analogous results are obtained for maps of class 𝒜r(D), r. We also establish the Oka property for sections of continuous or smooth fiber bundles over which are holomorphic over D and whose fiber enjoys the Convex Approximation Property (Theorem 1.7).

About the article

Received: 2006-07-07

Revised: 2006-07-12

Published Online: 2008-11-03

Published in Print: 2008-10-01


Citation Information: Forum Mathematicum, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/FORUM.2008.039.

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