Analyticity in the boundary of a pseudoconvex domain
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- by Alan V. Noell PDF
- Proc. Amer. Math. Soc. 94 (1985), 450-454 Request permission
Abstract:
Let $D$ be a bounded pseudoconvex domain with ${C^\infty }$ boundary in ${{\mathbf {C}}^n},{A^\infty }(D)$ the algebra of functions holomorphic in $D$ and ${C^\infty }$ up to the boundary, and $M$ a compact real-analytic manifold in the boundary which is integral for the complex structure of the boundary and which has no complex tangent vectors. A necessary and sufficient condition that each element of ${A^\infty }(D)$ be real-analytic on $M$ is that the germ of the complexification of $M$ be in the boundary. Examples indicate that the quasi-analyticity of ${A^\infty }(D)$ along $M$ is possible even in the absence of complex manifolds in the boundary.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 94 (1985), 450-454
- MSC: Primary 32F15; Secondary 32E25
- DOI: https://doi.org/10.1090/S0002-9939-1985-0787892-3
- MathSciNet review: 787892