Hadamard defines the “elementary solution” of the general linear partial differential equation of the second order, namely ( A ik , B i C being functions of the n variables x 1 , x 2 , .., x n , which may be regarded as coordinates in a space of n dimensions), to be one of those solutions which are infinite to as low an order as possible at a given point and on every bicharacteristic through that point.
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H. S. Ruse (1931) studied this question.
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