Ye, Zaifei The envelope of holomorphy of a truncated tube. (English) Zbl 0727.32006 Proc. Am. Math. Soc. 111, No. 1, 157-159 (1991). Let \(I=(-1,1)\subset {\mathbb{R}}\) and let \(h\in {\mathcal C}^{\infty}(I)\) be such that \(h(0)=0\), \(h'(0)=0\), and h attains both positive and negative values in any neighbourhood of 0. Let \(\Omega_ h\subset {\mathbb{C}}^ 2\) be the truncated tube domain which consists of all (z,w) such that Re \(z\in I\), Re \(w\in I\), Im \(z\in I\), Im \(w\in I\), and Re w\(>h(Re z)\). The author shows that the function h can be chosen so that the envelope of holomorphy of \(\Omega_ h\) does not contain a neighbourhood of 0. Reviewer: M.Klimek (Dublin) Cited in 2 Documents MSC: 32D10 Envelopes of holomorphy 32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010) 32D15 Continuation of analytic objects in several complex variables 31A05 Harmonic, subharmonic, superharmonic functions in two dimensions Keywords:CR-extensions; tube domains; envelope of holomorphy PDFBibTeX XMLCite \textit{Z. Ye}, Proc. Am. Math. Soc. 111, No. 1, 157--159 (1991; Zbl 0727.32006) Full Text: DOI References: [1] M. S. Baouendi and F. Trèves, A microlocal version of Bochner’s tube theorem, Indiana Univ. Math. J. 31 (1982), no. 6, 885 – 895. · Zbl 0505.32013 · doi:10.1512/iumj.1982.31.31060 [2] J.-M. Trépreau, Sur le prolongement holomorphe des fonctions C-R défines sur une hypersurface réelle de classe \?² dans \?\(^{n}\), Invent. Math. 83 (1986), no. 3, 583 – 592 (French). · Zbl 0586.32016 · doi:10.1007/BF01394424 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.