On holomorphic extension of functions on singular real hypersurfaces in ℂ n

Tejinder S. Neelon

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 26, 1-6

Abstract:

The holomorphic extension of functions defined on a class of real hypersurfaces in ℂ n with singularities is investigated. When n = 2 , we prove the following: every C 1 function on Σ that satisfies the tangential Cauchy-Riemann equation on boundary of { ( z , w ) ∈ ℂ 2 : | z | k < P ( w ) } , P ∈ C 1 , P ≥ 0 and P ≢ 0 , extends holomorphically inside provided the zero set P ( w ) = 0 has a limit point or P ( w ) vanishes to infinite order. Furthermore, if P is real analytic then the condition is also necessary.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:901061

DOI: 10.1155/S016117120100432X

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