A generalization of a theorem of Kühnel on globally defined analytic sets. Issue 11 (2nd November 2021)

• Record Type: Journal Article
• Authors: Abe, Makoto; Shima, Tadashi; Sugiyama, Shun
• Is Part Of: Complex variables and elliptic equations. Volume 66:Issue 11(2021)
• Page Start: 1937
• Page End: 1940
• Publication Date: 2021-11-02
• Subjects: K-complete complex space -- K-envelope -- Stein manifold; 32D10 -- 32D26 -- 32E10; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2020.1793968
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : Let X be a connected K -complete normal complex space. If for every closed discrete set A in X there exists a family F of holomorphic functions on X such that N ( F ) = A, then the K -envelope H ( X ) of holomorphy of X in the sense of Kerner (Math Ann. 1959;138:316–328) coincides with X .