The present monograph is devoted to the complex theory of
differential equations. Not yet a handbook, neither a simple
collection of articles, the book is a first attempt to present a
more or less detailed exposition of a young but promising branch of
mathematics, that is, the complex theory of partial differential
equations. Let us try to describe the framework of this theory.
First, simple examples show that solutions of differential
equations are, as a rule, ramifying analytic functions. and, hence,
are not regular near points of their ramification. Second, bearing
in mind these important properties of solutions, we shall try to
describe the method solving our problem. Surely, one has first to
consider differential equations with constant coefficients. The
apparatus solving such problems is well-known in the real the ory
of differential equations: this is the Fourier transformation. Un
fortunately, such a transformation had not yet been constructed for
complex-analytic functions and the authors had to construct by them
selves. This transformation is, of course, the key notion of the
whole theory."
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