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On an integral transformation of complex analytic functions. (English. Russian original) Zbl 0597.35003
Sov. Math., Dokl. 31, 125-127 (1985); translation from Dokl. Akad. Nauk SSSR 280, 553-556 (1985).
A construction is presented of an invertible integral transformation acting on analytic functions of several complex variables, which somewhat resembles the Radon transform and satisfies simple commutation relations with the operators of differentiation and of multiplication by independent variables. An application is given to a Cauchy problem for a linear PDE with constant coefficients with the initial data on an analytic surface.
Reviewer: P.Szeptycki
MSC:
35A22 Transform methods (e.g., integral transforms) applied to PDEs
35F15 Boundary value problems for linear first-order PDEs
32S45 Modifications; resolution of singularities (complex-analytic aspects)
44A05 General integral transforms
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