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METHODS OF FUNCTIONAL LINEAR ANALYSIS IN MATHEMATICAL PHYSICS

for every fixed point xoiD, with a similar requirement for the derivatives of u. Many researches were performed in this connection, however such a solution of the proposed problem fails to bring into evidence the functional dependence of u on the data / and g. We shall adopt a different enunciation of the problem. Let us suppose that the space 5 of all admissible functions is a Banach space and that (f,g) is a vector of a Banach space S'. Let us consider the linear transformation: