Abstract
Let E be a compact subset of C n and Φ some C n -valued mapping, holomorphic in a neighborhood of E, whose branch locus Σ intersects E. Let g be a C ∞ function which is ∂ -flat on Φ( E). Assume that the jet on E of the composite function g o Φ belongs to some sufficiently regular Carleman class { l!M l }. Then we give conditions which ensure the existence and allow an explicit definition of a sequence M + depending only on M, E and Φ, such that g satisfies optimal Carleman estimates { l!M l + } on Φ( E). The results can be applied to any mapping Φ with homogeneous components.
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