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International Journal of Mathematics and Mathematical Sciences
Volume 26, Issue 3, Pages 173-178

On holomorphic extension of functions on singular real hypersurfaces in n

Department of Mathematics, California State University San Marcos, San Marcos 92096, CA, USA

Received 3 January 2000

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The holomorphic extension of functions defined on a class of real hypersurfaces in n with singularities is investigated. When n=2, we prove the following: every C1 function on Σ that satisfies the tangential Cauchy-Riemann equation on boundary of {(z,w)2:|z|k<P(w)}, PC1, P0 and P0, 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.