Harmonic functions of two real or one complex variable, defined on star-shaped domains, are real parts of holomorphic functions. Mean value property and smoothness of holomorphic functions are thus, on star-shaped domains, transferred to harmonic functions. We use mentioned properties to solve Dirichlet problem for unit disk. Problem is the basis for introduction of Poisson kernel and Poisson integral. Uniqueness and existence of solution for Dirichlet problem, on bounded simply connected domains, lets us prove characterization of harmonic functions with mean value property. Mentioned characterization is crucial in proof of Schwarz reflection principle for harmonic functions.
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