We characterize CR functions on planar domains and real hypersurfaces in C2 in terms of analytic extendibility into attached analytic discs. It is done by studying propagation, from the boundary into interior, of degeneracy of CR foliations of solid torus-like manifolds. In particular, we answer, for smooth functions, two open questions mentioned in the title: about characterization of analytic functions in the complex plane and about characterization of boundary values of holomorphic functions in bounded domains in Cn. To cite this article: M. Agranovsky, C. R. Acad. Sci. Paris, Ser. I 343 (2006).
|Number of pages||4|
|Journal||Comptes Rendus Mathematique|
|State||Published - 15 Jul 2006|
Bibliographical noteFunding Information:
1 This work was partially supported by Israel Scientific Foundation, grant No. 279/02-01.