We study CR functions with values in a complex Fréchet space X. We prove a vector valued analog to a result by Baouendi and Trèves (Ann Math 113:387–421, 1981), i.e. any X-valued CR function of Teodorescu class B1 may be locally approximated by X-valued holomorphic functions on C^n. We show that any CR function u ∈ C^ω (M, X) on a real analytic CR hypersurface M ⊂ C^n admits a unique holomorphic extension f to some open neighborhood of M.
Baouendi–Trèves approximation theorem for CR functions with values in a complex Fréchet space
DRAGOMIR, Sorin;
2012-01-01
Abstract
We study CR functions with values in a complex Fréchet space X. We prove a vector valued analog to a result by Baouendi and Trèves (Ann Math 113:387–421, 1981), i.e. any X-valued CR function of Teodorescu class B1 may be locally approximated by X-valued holomorphic functions on C^n. We show that any CR function u ∈ C^ω (M, X) on a real analytic CR hypersurface M ⊂ C^n admits a unique holomorphic extension f to some open neighborhood of M.File in questo prodotto:
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