Möbius function of coordinate hyperplanes in complex ellipsoids
HTML articles powered by AMS MathViewer
- by Witold Jarnicki PDF
- Proc. Amer. Math. Soc. 132 (2004), 3243-3250 Request permission
Abstract:
For $p_1,\dots ,p_n>0$, let $\mathbb {E}=\{z\in \mathbb {C}^n:\sum _{j=1}^n|z_j|^{2p_j}<1\}$ be a complex ellipsoid. We present effective formulas for the generalized Möbius and Green functions $m_{\mathbb {E}}(A,\cdot )$, $g_{\mathbb {E}}(A,\cdot )$ in the case where $A:=\{z\in \mathbb {E}:z_1\cdots z_k=0\}$ ($1\leq k\leq n$).References
- Marek Jarnicki, Witold Jarnicki, and Peter Pflug, On extremal holomorphically contractible families, Ann. Polon. Math. 81 (2003), no. 2, 183–199. MR 1976197, DOI 10.4064/ap81-2-8
- Marek Jarnicki and Peter Pflug, Invariant distances and metrics in complex analysis, De Gruyter Expositions in Mathematics, vol. 9, Walter de Gruyter & Co., Berlin, 1993. MR 1242120, DOI 10.1515/9783110870312
- Finnur Lárusson and Ragnar Sigurdsson, Plurisubharmonic functions and analytic discs on manifolds, J. Reine Angew. Math. 501 (1998), 1–39. MR 1637837, DOI 10.1515/crll.1998.078
- Nguyen Quang Dieu, Continuity of pluricomplex Green functions with poles along a hypersurface, preprint.
Additional Information
- Witold Jarnicki
- Affiliation: Jagiellonian University, Institute of Mathematics, Reymonta 4, 30-059 Kraków, Poland
- Address at time of publication: Universität Osnabrück, Fachbereich Mathematik/Informatik, Albrechtstraße 28, 49069 Osnabrück, Germany
- Email: wmj@im.uj.edu.pl
- Received by editor(s): June 23, 2003
- Published electronically: June 17, 2004
- Additional Notes: The author was supported in part by KBN grant no. 2 P03A 015 22.
- Communicated by: Mei-Chi Shaw
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 3243-3250
- MSC (2000): Primary 32F45, 32U35
- DOI: https://doi.org/10.1090/S0002-9939-04-07546-X
- MathSciNet review: 2073298