Abstract
Let M M be a lineally convex hypersurface of C n \mathbb C^n of finite type, 0 ∈ M 0\in M . Then there exist non-trivial smooth CR functions on M M that are flat at 0 0 , i.e. whose Taylor expansion about 0 0 vanishes identically. Our aim is to characterize the rate at which flat CR functions can decrease without vanishing identically. As it turns out, non-trivial CR functions cannot decay arbitrarily fast, and a possible way of expressing the critical rate is by comparison with a suitable exponential of the modulus of a local peak function.
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