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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). [3] V. P. Maslov, ?The FourierA-transform,? Tr. Mosk. Inst. Elektr. Mashinostr., 55-99 (1972). [4] B. Yu. Sternin and V. E. Shatalov, ?An integral transform of complex analytic functions,? Izv. Akad. Nauk SSSR., Ser. Mat.,50, No. 5, 1054-1076 (1986). [5] B. Yu. Sternin and V. E. Shatalov, ?An integral representation and a transformation of complex analytic functions connected with it,? Dokl. Akad. Nauk SSSR,298, No. 1, 44-48 (1988). [6] B. Yu. Sternin and V. E. Shatalov, ?Differential equations on complex-analytic manifolds and the canonical Maslov operator,? Usp. Mat. Nauk,43, No. 3, 97-124 (1988). · Zbl 0663.35007 [7] J. Leray, Differential and Integral Calculus on Complex-Analytic Manifolds [Russian translation], IL, Moscow (1965). [8] J. Leray, L. Garding, and T. Kotake, The Cauchy Problem [Russian translation], Mir, Moscow (1967). [9] F. Pham, Introduction to the Topological Study of Landau Singularities [Russian translation], Mir, Moscow (1980).
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