On holomorphic extension of functions on singular real hypersurfaces in ℂn
The holomorphic extension of functions defined on a class of real hypersurfaces in ℂn 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)∈ℂ2:|z|k<P(w)}, P∈C1, P≥0 and P≢0, extends...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120100432X |
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| _version_ | 1832560602015334400 |
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| author | Tejinder S. Neelon |
| author_facet | Tejinder S. Neelon |
| author_sort | Tejinder S. Neelon |
| collection | DOAJ |
| description | The holomorphic extension of functions defined on a class of real hypersurfaces in ℂn 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)∈ℂ2:|z|k<P(w)}, P∈C1, 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. |
| format | Article |
| id | doaj-art-6ee05e6b2e684a4689ff2a895cb56a80 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-6ee05e6b2e684a4689ff2a895cb56a802025-02-03T01:27:12ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-0126317317810.1155/S016117120100432XOn holomorphic extension of functions on singular real hypersurfaces in ℂnTejinder S. Neelon0Department of Mathematics, California State University San Marcos, San Marcos 92096, CA, USAThe holomorphic extension of functions defined on a class of real hypersurfaces in ℂn 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)∈ℂ2:|z|k<P(w)}, P∈C1, 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.http://dx.doi.org/10.1155/S016117120100432X |
| spellingShingle | Tejinder S. Neelon On holomorphic extension of functions on singular real hypersurfaces in ℂn International Journal of Mathematics and Mathematical Sciences |
| title | On holomorphic extension of functions on singular real hypersurfaces in ℂn |
| title_full | On holomorphic extension of functions on singular real hypersurfaces in ℂn |
| title_fullStr | On holomorphic extension of functions on singular real hypersurfaces in ℂn |
| title_full_unstemmed | On holomorphic extension of functions on singular real hypersurfaces in ℂn |
| title_short | On holomorphic extension of functions on singular real hypersurfaces in ℂn |
| title_sort | on holomorphic extension of functions on singular real hypersurfaces in cn |
| url | http://dx.doi.org/10.1155/S016117120100432X |
| work_keys_str_mv | AT tejindersneelon onholomorphicextensionoffunctionsonsingularrealhypersurfacesincn |