Topic
Hartogs' theorem
About: Hartogs' theorem is a research topic. Over the lifetime, 35 publications have been published within this topic receiving 182 citations.
Papers
TL;DR: The envelope of holomorphy of Stein manifolds is studied in this article, where it is shown that a function on which it is separately analytic, i.e. for which is analytic in in in for any fixed and analytic in ∆ for every fixed, extends to an analytic function in some open neighborhood of which is the envelope of HOLM of.
Abstract: Let and be arbitrary Stein manifolds, and compact sets, and . Under certain general hypotheses it is proved that a function on which is separately analytic, i.e. for which is analytic in in for any fixed and analytic in in for any fixed , extends to an analytic function in some open neighborhood of which is the envelope of holomorphy of .The envelope of holomorphy of is studied in those cases in which has no open envelope of holomorphy.Bibliography: 26 titles.
37 citations
1 Jul 2006
TL;DR: In this article, Hartogs' separate analyticity theorem is extended to functions holomorphic along holomorphic curves that form mutually transversal foliations of the domain of definition of these functions.
Abstract: Hartogs’ separate analyticity theorem is extended to functions holomorphic along holomorphic curves that form mutually transversal foliations of the domain of definition of these functions.
19 citations
TL;DR: In this paper, it was shown that the set of all complex lines passing through a germ of a generating manifold is sufficient for any continuous function f defined on the boundary of a bounded domain D ⊂ ℂn with connected smooth boundary and having the holomorphic one-dimensional extension property along all lines from \( \mathfrak{L}_\Gamma \) to admit a holomorphic extension to D as a function of many complex variables.
Abstract: It is shown that the set \( \mathfrak{L}_\Gamma \) of all complex lines passing through a germ of a generating manifold Γ is sufficient for any continuous function f defined on the boundary of a bounded domain D ⊂ ℂn with connected smooth boundary and having the holomorphic one-dimensional extension property along all lines from \( \mathfrak{L}_\Gamma \) to admit a holomorphic extension to D as a function of many complex variables.
16 citations
11 Oct 2014
TL;DR: In this article, a multidimensional octonion analysis is initiated, which extends the theory of several complex variables, such as the Bochner-Martinelli formula, Cauchy-Riemann equations, and Hartogs principle, to the non-commutative and non-associative realm.
Abstract: The octonions are distinguished in the $$M$$
-theory in which Universe is the usual Minkowski space $${\mathbb {R}}^4$$
times a $$G_2$$
manifold of very small diameter with $$G_2$$
being the automorphism group of the octonions The multidimensional octonion analysis is initiated in this article, which extends the theory of several complex variables, such as the Bochner–Martinelli formula, the theory of non-homogeneous Cauchy–Riemann equations, and the Hartogs principle, to the non-commutative and non-associative realm
14 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2019 | 2 |
| 2018 | 1 |
| 2016 | 1 |
| 2015 | 2 |
| 2014 | 4 |
| 2012 | 2 |