Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



$ C\sp{k}$, weakly holomorphic functions on analytic sets

Author: Joseph Becker
Journal: Proc. Amer. Math. Soc. 39 (1973), 89-93
MSC: Primary 32K15; Secondary 32B10
MathSciNet review: 0322214
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ V$ be a complex analytic set and $ p \in V$. Let $ \mathcal{O}(V),\tilde{\mathcal{O}}(V)$, and $ {C^k}(V)$ denote respectively the rings of germs of holomorphic, weakly holomorphic, and $ k$-times continuously differentiable functions on $ V$. Spallek proved that there exists sufficiently large $ k$ such that $ {C^k}(V) \cap \tilde{\mathcal{O}}(V) = \mathcal{O}(V)$. In this paper I give a new proof of this result for curves and hypersurfaces which also establishes that the conduction number of the singularity is an upper bound for $ k$. This estimate also holds for any pure dimensional variety off of a subvariety of codimension two.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32K15, 32B10

Retrieve articles in all journals with MSC: 32K15, 32B10

Additional Information

Keywords: $ {C^k}$, weakly holomorphic, conduction number
Article copyright: © Copyright 1973 American Mathematical Society