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Newton polyhedra and estimation of oscillating integrals. (English) Zbl 0351.32011

MSC:
32SxxSingularities (analytic spaces)
32B10Germs of analytic sets, local parametrization
52BxxPolytopes and polyhedra
57R70Critical points and critical submanifolds
26E10C real functions, quasi-analytic real functions
References:
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[10]O. Zariski, ”Contributions to the problem of equisingularities,” C. I. M. E., Varenna (1969) (Edizioni Cremonese Roma (1970)).
[11]A. G. Kushnirenko, ”Newton polyhedron and Milnor numbers,” Funktsional’. Analiz Ego Prilozhen.,9, No. 1, 74-75 (1975).
[12]O. Zariski, ”Studies in equisingularity,” I, Amer. J. Math.,87, 507-536 (1965). · Zbl 0132.41601 · doi:10.2307/2373019
[13]D. N. Bernshtein, ”The number of roots of a system of equations,” Funktsional’. Analiz Ego Prilozhen.,9, No. 3, 1-4 (1975). · Zbl 0395.60076 · doi:10.1007/BF01078167
[14]O. Zariski, ”Studies in equisingularity,” II, Amer. J. Math.,87, 972-1006 (1965). · Zbl 0146.42502 · doi:10.2307/2373257
[15]H. Hironaka, Course on Singularities, C. I. M. E., Bressanone, June (1974).
[16]V. I. Arnol’d, ”Critical points of smooth functions and their normal forms,” Usp. Matem. Nauk,30, No. 5, 3-65 (1975).
[17]V. I. Arnol’d, ”Normal forms of functions near degenerate critical points, the Weyl groups of Ak, Dk, Ek, and Lagrangian singularities,” Funktsional’. Analiz Ego Prilozhen.,6, No. 4, 3-25 (1972).