Boundary uniqueness theorems in C n extbf {C}^ n Academic Article uri icon

abstract

  • Let n-dimensional manifolds Γk, k = 1,2,…, be given in a smoothly bounded domain Ω ⊂ Cn. Assume that the Γk “converge” to an n-dimensional, totally real manifold Γ ⊆ ∂Ω and that a function f analytic in Ω has the property that its traces k on Γk have distributional limit zero as k → ∞ (or assume that fk → 0 pointwise). Then under the assumption that f is polynomially bounded near P ∈ Γ by (dist (z,∂Ω))-1 we conclude that f is identically zero. © 1986 American Mathematical Society.

author list (cited authors)

  • Cima, J. A., & Straube, E. J.

citation count

  • 0

publication date

  • January 1986