Abstract
The equations considered in this paper are linear systems of as many partial differential equations as there are unknown functions, of arbitrary order, and of coefficients analytic in the independent variables (xi, , x). We shall prove certain theorems regarding the region of existence of analytic solutions and the relation between the mobile singularities and the characteristics of the system. Our theorems have been proved in the case of one equation in two independent variables by Le Roux (Annales Scientifiques de l'Ecole Normale Superieure, (3), vol. 12 (1895), p. 227; Journal de Mathematiques, (5), vol. 4 (1898), p. 402), and in the real region under the same restrictions by Delassus (Annales Scientifiques de l'Ecole Normale Superieure, loc. cit., Supplement p. 53). They have been extended to equations in n independent variables by these authors, and by Hadamard (Lectures on Cauchy's Problem, Yale University Press, 1923, p. 72), but only under the severest restrictions, and by methods which do not admit of generalization. We shall consider the system
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