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The Laplace-Radon integral transform and its application to an inhomogeneous Cauchy problem in a complex space. (English. Russian original) Zbl 0666.44004
Differ. Equations 24, No. 1, 131-137 (1988); translation from Differ. Uravn. 24, No. 1, 167-174 (1988).
The Laplace-Radon transform, introduced previously, gives explicitely the solution of a Cauchy problem for equations with constant coefficients and vanishing data on a given complex subvariety of codimension one. The authors generalize this result to a problem with non-zero Cauchy data. The solution is found in the class of analytic multiple-valued functions and the method gives a closed formula for it.
Reviewer: J.Souček

44A15 Special integral transforms (Legendre, Hilbert, etc.)
44A10 Laplace transform
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.