Abstract
This paper is primarily a study of generalized notions of envelope of holomorphy and holomorphic convexity for special (algebraically restricted) subsets of C n {{\mathbf {C}}^n} and in part for arbitrary subsets of C n {{\mathbf {C}}^n} . For any special set S in C n {{\mathbf {C}}^n} , we show that every function holomorphic in a neighborhood of S not only can be holomorphically continued but also holomorphically extended to a neighborhood in C n {{\mathbf {C}}^n} of a maximal set S ~ \tilde {S} , the “envelope of holomorphy” of S, which is also a special set of the same type as S. Formulas are obtained for constructing S ~ \tilde {S} for any special set S. “Holomorphic convexity” is characterized for these special sets. With one exception, the only topological restriction on these special sets is connectivity. Examples are given which illustrate applications of the theorems and help to clarify the concepts of “envelope of holomorphy” and “holomorphic convexity."
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
