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On an integral transform of complex-analytic functions. (English. Russian original) Zbl 0806.35004
Proc. Steklov Inst. Math. 193, 193-196 (1993); translation from Tr. Mat. Inst. Steklova 193, 174-177 (1992).
An integral transform acting in a space of multiple-valued analytic functions and commuting with the operators of differentiation and multiplication by an independent variable is defined. This transform works in the theory of differential equations on complex analytic spaces, e.g. it supplies exact formulae for the solution of the Cauchy problem (for equations with constant coefficients) with initial data that are defined on an arbitrary analytic set \(X\) of codimension 1. In the special case of real functions (when \(X\) is empty) it becomes the usual Fourier transform of homogeneous functions. The transform includes, e.g., the classical Radon transform and the Fourier-Maslov \(\partial/ \partial \xi\) transform.
For the entire collection see [Zbl 0785.00035].
Reviewer: J.Fuka (Praha)
35A22 Transform methods (e.g., integral transforms) applied to PDEs
32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)