Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-08T06:33:06.187Z Has data issue: false hasContentIssue false
  • English
  • Français

On Holomorphic Extension from the Boundary

Published online by Cambridge University Press:  22 January 2016

Kiyoshi Shiga
Kiyoshi Shiga*
Affiliation:
Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let D be a bounded domain of the complex n-space Cn(n≥2), or more generally a pair (M,D) a finite manifold (cf. Definition 2.1), and we assume the boundary ∂D is a smooth and connected submanifold. It is well known by Hartogs-Osgood’s theorem that every holomorphic function on a neighbourhood of ∂D can be continued holomorphically to D. Generalizing the above theorem we shall prove that if a differentiable function on ∂D satisfies certain conditions which are satisfied for the trace of a holomorphic function on a neighbourhood of ∂D, then it can be continued holomorphically to D (Theorem 2-5). The above conditions will be called the tangential Cauchy Riemann equations.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 42 , March 1971 , pp. 57 - 66
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

[1] Hörmander, L. An introduction to complex analysis in several variables. Van Norstrand 1966.Google Scholar
[2] Kasahara, K. On Hartogs-Osgood’s theorem for Stein Spaces., J. Math. Soci. Japan 17 (1965) pp. 297–314.Google Scholar
[3] Matsushima, Y. and Morimoto, A. Sur certains espaces fibrés holomorphes sur une variété de Stein., Bull. Soci. Math. France 88, 1960 pp. 137–155.Google Scholar