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Let  X  be a compact coherent real analytic subvariety of. It is shown that a continuous linear operator which extends real analytic functions on  X  to real analytic functions onexists if and only if  X  is of type PL, which means that in every point of  X  the local complexification satisfies Hörmander's local Phragmén-Lindelöf condition. This is in particular true if  X  is a manifold.

Extension operators for real analytic functions on compact subvarieties of