Geodesic
Asymptotic expansions of integrals in complex and real regions
Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 207-236 Cet article a éte moissonné depuis la source Math-Net.Ru

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Asymptotic expansions are studied for integrals of holomorphic forms over cycles in the Milnor fibration close to a critical level surface of a holomorphic function. Some regular features are found for the set of exponents in such expansions, and computational results are given. Asymptotic expansions are also considered for real integrals connected with analytic functions. A connection is established between expansions of integrals in a complex region and a real region. Bibliography: 30 titles. 
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     author = {V. P. Palamodov},
     title = {Asymptotic expansions of integrals in complex and real regions},
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V. P. Palamodov. Asymptotic expansions of integrals in complex and real regions. Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 207-236. http://geodesic.mathdoc.fr/item/SM_1986_55_1_a12/

[1] Malgrange B., “Integrates asymptotiques et monodromie”, Ann. Ec. Norm. Sup., 7 (1974), 405–430 | MR | Zbl

[2] Lê Dûng Tráng, “The geometry of the monodromy theorem”, Geometry and Analysis, Bombay, 1978

[3] Hironaka H., “Resolution of singularities of an algebraic variety over a field of characteristic zero”, Ann. of Math., 79:1 (1964), 109–180 ; 79:2 (1964), 205–320 ; Хиронака X., “Разрешение особенностей алгебраических многообразий над полями характеристики нуль”, Математика (сб. переводов), 9:6 (1965), 3; 10:1 (1966), 3 ; 10:2 (1966), 3 | DOI | MR | DOI | MR | MR

[4] Palamodov V. P., “Asimptotiki ostsilliruyuschikh integralov s izolirovannoi statsionarnoi tochkoi fazy”, DAN SSSR, 250:6 (1980), 1321 | MR | Zbl

[5] Steenbrink J., “Mixed Hodge structure on vanishing cohomology”, Nordic Summer School, Symp. in Math., Oslo, 1976, 525 | MR

[6] Varchenko A. N., “Gauss–Manin connection of isolated singular point and Bernstein polynomial”, Bull. Soc. Math., Ser. 2, 104:2 (1980), 205–223 | MR | Zbl

[7] Saito K., “Quasihomogene isolierte Singularitäten von Hyperflächen”, Invent Math., 14 (1971), 123–142 | DOI | MR | Zbl

[8] Malgrange B., “Le polynome de Bernstein d'une singularite isolee”, Lecture Notes in Math., no. 459, Springer-Verlag, Berlin–Heidelberg–New York, 1974, 98 | MR

[9] Saito K., “The higher residues pairings for a family of hypersurface singular points”, Proc. Symp. Pure Math., 40, part 2 (1983), 441–463 | MR | Zbl

[10] Guzev S. V., “O spektre nekvaziodnorodnykh polinomov”, Funkts. analiz i ego pril., 18:1 (1984), 70 | MR | Zbl

[11] Jeanquartier D., “Développement asymptotique de la distribution de Dirac”, C. R. Acad. Sc. Paris, 271 (1970), 1159 | MR | Zbl

[12] Yano T., “b-functions and exponents of hypersurface isolated singularities”, Proc. Symp. Pure Math., 40, part. 2 (1983), 641 | MR | Zbl

[13] Yano T., “On the theory of b-functions”, Publ. RIMS, Kyoto Univ., 14:1 (1978), 111 | DOI | MR | Zbl

[14] Varchenko A. N., “Kompleksnyi pokazatel osobosti ne menyaetsya vdol strata $\mu=\operatorname{const}$”, Funkts. analiz i ego pril., 16:1 (1982), 1 | MR | Zbl

[15] Loojienga E., “A period mapping for certain semi-universal deformations”, Compositio Math., 80:3 (1975), 299 | MR

[16] Brieskorn E., “Die Monodromie der isolierten Singularitäten von Hyperflächen”, Manuscripta Math., 2 (1970), 103 ; Брискорн Э., “Монодромия изолированных особенностей гиперповерхностей”, Математика (сб. переводов), 15:4 (1971), 130 | DOI | MR | Zbl

[17] Sebastiani M., “Preuve d'une conjecture de Brieskorn”, Manuscripta Math., 2 (1970), 301 | DOI | MR | Zbl

[18] Gabrielov A. M., “Matritsy peresechenii dlya nekotorykh osobennostei”, Funkts. analiz i ego pril., 7:3 (1973), 18 | MR | Zbl

[19] Hartshorne R., “Residues and Duality”, Lecture Notes in Math., no. 20, Springer-Verlag, Berlin–Heidelberg–New York, 1966 | MR | Zbl

[20] Griffits F., Kharris Dzh., Printsipy algebraicheskoi geometrii, T. 2, Mir, M., 1982 | MR

[21] Arnold V. I., “Kriticheskie tochki gladkikh funktsii i ikh normalnye formy”, UMN, 30:5 (1975), 3 | Zbl

[22] Gelfand I. M., Shilov G. E., Obobschennye funktsii i deistviya nad nimi, Fizmatgiz, M., 1958 | Zbl

[23] Riesz M., “L'integrale de Riemann – Liouville et le probleme de Cauchy”, Acta Math., 81 (1949), 1 | DOI | MR | Zbl

[24] Fedoryuk M. V., “Neodnorodnye obobschennye funktsii dvukh peremennykh”, Matem. sb., 49(91) (1959), 431 | Zbl

[25] Bernshtein I. N., Gelfand S. I., “Meromorfnaya funktsiya $f^{\lambda}$”, Funkts. analiz i ego pril., 3:1 (1969), 84 | MR

[26] Atijah M. F., “Resolution of singularities and division of distributions”, Comm. Pure Appl. Math., 23:2 (1976), 145 | DOI

[27] Scherk J., “Isolated singular points and the Gauss–Manin connections”, D. Phil. Thesis, Exeter College, Oxford, 1977

[28] Bruhat F., Cartan H., “Sur la structure des sous-ensembles analitiques reels”, C. R. Ac. Sci. Paris, Ser. A, 244 (1957), 988–990 | MR | Zbl

[29] Lejeune M., Teissier B., “Quelques calcules utiles pour la résolution de singularites”, Seminaire Ecole Polytechnique, Centre de Math, de l'Ecole Polytechnique, 1972, 130

[30] Mather J. N., Yau S. S. T., “Classifikation of isolated hypersurface singularities by their moduli algebra”, Invent. Math., 69 (1982), 243–251 | DOI | MR | Zbl