ON A UNIQUENESS CONDITION FOR CR FUNCTIONS ON HYPERSURFACES

摘要

Let f be a smooth CR function on a smooth hypersurface M ?C n , such that f vanishes to infinite order along a C ∞ -smooth curve γ ? M. Assume that for each q ∈ γ there exists a truncated double cone C at q in M, such that at least one of the following three conditions holds true: (a) There is a constant θ ∈ R, such that C ? { ? Re(e iθ f) ? ≤ ? Im(e iθ f) ? }. (b) C ? {Ref ≥ 0}. (c) |f(z)| |z?q| → 0, z → q, z ∈ C. Then f vanishes on an M-open neighborhood of γ.