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

Let n n -dimensional manifolds k , k = 1 , 2 , {Gamma _k},,k = 1,2, ldots , be given in a smoothly bounded domain C n Omega subset {{mathbf {C}}^n} . Assume that the k {Gamma _k} "converge" to an n n -dimensional, totally real manifold Gamma subseteq partial Omega and that a function f f analytic in Omega has the property that its traces f k {f_k} on k {Gamma _k} have distributional limit zero as k k o infty (or assume that f k 0 {f_k} o 0 pointwise). Then under the assumption that