Harmonic conjugate
Concept in mathematics / From Wikipedia, the free encyclopedia
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For geometric conjugate points, see Projective harmonic conjugate.
"Conjugate function" redirects here. For the convex conjugate of a function, see Convex conjugate.
In mathematics, a real-valued function defined on a connected open set is said to have a conjugate (function) if and only if they are respectively the real and imaginary parts of a holomorphic function of the complex variable That is, is conjugate to if is holomorphic on As a first consequence of the definition, they are both harmonic real-valued functions on . Moreover, the conjugate of if it exists, is unique up to an additive constant. Also, is conjugate to if and only if is conjugate to .