K-holomorphic functions have definable real parts precisely when they are definable and their real parts are strongly R-analytic, with a full if-and-only-if characterization holding in the semialgebraic o-minimal structure.
Carbone: Holomorphic functions with Nash real part
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$K$-holomorphic functions with definable real part
K-holomorphic functions have definable real parts precisely when they are definable and their real parts are strongly R-analytic, with a full if-and-only-if characterization holding in the semialgebraic o-minimal structure.