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Fourier-Maslov transform in the space of multivalued analytic functions. (English. Russian original) Zbl 0755.32003
Math. Notes 49, No. 6, 627-635 (1991); translation from Mat. Zametki 49, No. 6, 107-118 (1991).
The authors define some integral transform in the space of multivalent analytic functions, which is the natural “complex” analog of “real”. A Fourier transform for the smooth situation was introduced by V. P. Maslov in 1965. The authors prove the main properties of the Fourier- Maslov transform about inversion and the theorem about computation.

MSC:
32A10 Holomorphic functions of several complex variables
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
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References:
[1] V. P. Maslov, Theory of Perturbations and Asymptotic Methods [in Russian], Mosk. Gos. Univ., Moscow (1965).
[2] V. P. Maslov, Operator Methods [in Russian], Nauka, Moscow (1973).
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