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Method of a stationary phase for the Laplace-Radon transforms. (English. Russian original) Zbl 0788.44002
Math. Notes 51, No. 4, 401-407 (1992); translation from Mat. Zametki 51, No. 4, 109-118 (1992).
The paper contains detailed proofs of results concerning the asymptotic expansion of the Laplace-Radon transform, which were already announced earlier [Dokl. Akad. Nauk SSSR 317, No. 6, 1311-1314 (1991; Zbl 0753.30027); and Mat. Zametki 49, No. 6, 107-118 (1991; Zbl 0755.32003)].
Reviewer: L.Berg (Rostock)
44A12 Radon transform
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
Full Text: DOI
[1] V. P. Maslov, Asymptotic Methods in Perturbation Theory [in Russian], Nauka, Moscow (1988). · Zbl 0653.35002
[2] M. V. Fedoryuk, The Saddle-Point Method [in Russian], Nauka, Moscow (1984). · Zbl 0582.35024
[3] A. S. Mishchenko, B. Yu. Sternin, and V. E. Shatalov, Lagrangian Manifolds and the Maslov Operator, Springer-Verlag, Berlin-New York (1990). · Zbl 0727.58001
[4] J. Leray, ?Differential and integral calculus on complex analytic manifolds,? Bull. Soc. Math. Fr.,87, 81-180 (1959).
[5] F. Pham, Introduction a L’étude Topologique des Singularités de Landau [in French], Memorial des Sciences Mathématique, Gauthier-Villars, Paris (1967).
[6] B. Yu. Sternin and V. E. Shatalov, ?Differential equations on complex-analytic manifolds. and the Maslov operator,? Usp. Mat. Nauk,43, No. 3, 99-124 (1988). · Zbl 0663.35007
[7] B. Yu. Sternin and V. E. Shatalov, ?A form of an asymptotic expansion of an integral in complex analysis,? Dokl. Akad. Nauk SSSR,317, No. 6, 1311-1314 (1991).
[8] B. Yu. Sternin and V. E. Shatalov, ?A Fourier-Maslov transform in the space of many-valued analytic functions,? Mat. Zametki,49, No. 6, 107-118 (1991). · Zbl 0755.32003
[9] B. Y. Sternin and V. E. Shatalov, ?An integral representation and associated transform of complex-analytic functions,? Dokl. Akad. Nauk SSSR,298, No. 1, 44-48 (1988). · Zbl 0688.32006
[10] B. Yu. Sternin and V. E. Shatalov, ?The Laplace-Radon integral transform and its application to a nonhomogeneous Cauchy problem in a complex space,? Differents. Uravn.,24, No. 1, 167-174 (1988).
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