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In mathematics, precisely in the theory of functions of several complex variables, a pluriharmonic function is a real valued function which is locally the real part of a holomorphic function of several complex variables. Sometimes a such function is referred as ''n''-harmonic function, where ''n'' ≥ 2 is the dimension of the complex domain where the function is defined.〔See for example and . calls such functions "''fonctions biharmoniques''", irrespective of the dimension ''n'' ≥ 2 : note also that his paper is perhaps the older one in which the pluriharmonic operator is expressed using the first order partial differential operators now called Wirtinger derivatives.〕 However, in modern expositions of the theory of functions of several complex variables〔See for example the popular textbook by and the advanced (even if a little outdated) monograph by .〕 it is preferred to give an equivalent formulation of the concept, by defining pluriharmonic function a complex valued function whose restriction to every complex line is an harmonic function respect to the real and imaginary part of the complex line parameter. ==Formal definition== . Let be a complex domain and be a (twice continuously differentiable) function. The function is called pluriharmonic if, for every complex line : formed by using every couple of complex tuples , the function : is a harmonic function on the set :. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「pluriharmonic function」の詳細全文を読む スポンサード リンク
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