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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Analyticity in the boundary of a pseudoconvex domain

Author: Alan V. Noell
Journal: Proc. Amer. Math. Soc. 94 (1985), 450-454
MSC: Primary 32F15; Secondary 32E25
MathSciNet review: 787892
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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.

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Keywords: Pseudoconvex domain, integral manifold, complexification
Article copyright: © Copyright 1985 American Mathematical Society