On Analytic Interpolation Manifolds in Boundaries of Weakly Pseudoconvex Domains
نویسنده
چکیده
Let Ω be a bounded, weakly pseudoconvex domain in Cn, n ≥ 2, with real-analytic boundary. A real-analytic submanifold M ⊂ ∂Ω is called an analytic interpolation manifold if every real-analytic function on M extends to a function belonging to O(Ω). We provide sufficient conditions for M to be an analytic interpolation manifold. We give examples showing that neither of these conditions can be relaxed, as well as examples of analytic interpolation manifolds lying entirely within the set of weakly pseudoconvex points of ∂Ω.
منابع مشابه
Hartogs Type Theorems for CR L functions on Coverings of Strongly Pseudoconvex Manifolds
We prove an analog of the classical Hartogs extension theorem for CR L2 functions defined on boundaries of certain (possibly unbounded) domains on coverings of strongly pseudoconvex manifolds. Our result is related to a question formulated in the paper of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds.
متن کاملOn Peak-interpolation Manifolds for A(ω) for Convex Domains in C
Let Ω be a bounded, weakly convex domain in C, n ≥ 2, having real-analytic boundary. A(Ω) is the algebra of all functions holomorphic in Ω and continuous upto the boundary. A submanifold M ⊂ ∂Ω is said to be complex-tangential if Tp(M) lies in the maximal complex subspace of Tp(∂Ω) for each p ∈ M. We show that for real-analytic submanifolds M ⊂ ∂Ω, if M is complex-tangential, then every compact...
متن کاملComplete Localization of Domains with Noncompact Automorphism Groups
We prove a characterization of the domains in en with an automorphism orbit accumulating at a boundary point at which the boundary is real analytic and convex up to a biholomorphic change of local coordinates. This result generalizes the well-known Wong-Rosay theorem on strongly pseudoconvex domains to the case of locally convex domains with real analytic boundaries.
متن کاملHolomorphic Functions of Slow Growth on Coverings of Pseudoconvex Domains in Stein Manifolds
We apply the methods developed in [Br1] to study holomorphic functions of slow growth on coverings of pseudoconvex domains in Stein manifolds. In particular, we extend and strengthen certain results of Gromov, Henkin and Shubin [GHS] on holomorphic L2 functions on coverings of pseudoconvex manifolds in the case of coverings of Stein manifolds.
متن کاملSome Applications of the Kohn{rossi Extension Theorems
We prove extension results for meromorphic functions by combining the Kohn-Rossi extension theorems with Andreotti's theory on the algebraic and analytic dependence of meromorphic functions on pseudoconcave manifolds. Versions of Kohn-Rossi theorems for pseudo-convex domains are included.
متن کامل