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The set of harmonic functions on a given open setembre '' U '' can be seen as the [[Kernel (algebra)|nucli]] of the [[Laplace operator]] Δ and is therefore a [[vector space]] over ''' R ''': sums, differences and scalar multiples of harmonic functions are again harmonic.
Si '' f '' is a harmonic function on '' U '', then all [[partial derivative]]
In several ways, the harmonic functions are real analogues to [[holomorphic function]] s. All harmonic functions are [[analytic function|analytic]], ie they can be locally expressed as [[power sèries]]. This is a general fact about [[elliptic operator]] s, of which the Laplacian is a major example.
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