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The Laplace-Radon transformation in complex analysis and its applications. I. (English) Zbl 0904.32001
Summary: A new integral transformation in spaces of ramified analytic functions is proposed. This transformation can be used to solve a wide class of problems from the theory of differential equations on complex analytic manifolds. For example, it yields complete formulas for solutions of equations with constant coefficients and makes it possible to construct asymptotics in smoothness for solutions of equations with variable coefficients in neighborhoods of singularities. The transformation can also be applied to the solvability problem and to solving certain problems of mathematical physics.
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
44A12 Radon transform
32L25 Twistor theory, double fibrations (complex-analytic aspects)