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arXiv · 2406.06431

CR functions at CR singularities: approximation, extension, and hulls

Jiri Lebl·Alan Noell·Sivaguru Ravisankar
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Abstract

We study three possible definitions of the notion of CR functions at CR singular points, their extension to a fixed-neighborhood of the singular point, and analogues of the Baouendi--Tr\`eves approximation in a fixed neighborhood. In particular, we give a construction of certain disc hulls, which, if large enough, give the fixed-neighborhood extension and approximation properties. We provide many examples showing the distinctions between the classes and the various properties studied.

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Jiri Lebl, Alan Noell, Sivaguru Ravisankar. 2024-06-10. CR functions at CR singularities: approximation, extension, and hulls. https://doi.org/10.1007/s12220-025-02116-y

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