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Vanishing theorems in asymptotic analysis. II. (English) Zbl 0565.32014
In a previous paper (see the review above) the author announced some vanishing theorems in asymptotic analysis in several variables. More theorems of that nature are announced in this note. For complete proofs of these theorems see the author’s book: ”Asymptotic analysis for integrable connections with irreguar singular points”, Lect. Notes Math. 1075 (1984; Zbl 0546.58003)].
Reviewer: D.Sundararaman

32L20 Vanishing theorems
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
58J10 Differential complexes
Full Text: DOI
[1] Bingener, J.: Uber Formale Komplexe Raume. Manuscripta Math., 253-293 (1978) (cf. Math. Review 58 #11492 by C. Banica). · Zbl 0381.32015 · doi:10.1007/BF01167833 · eudml:154547
[2] Majima, H.: Vanishing theorems in asymptotic analysis. Proc. Japan Acad., 59A, 146-149 (1983). · Zbl 0565.32013 · doi:10.3792/pjaa.59.146
[3] Majima, H.: V-Poincare’s lemma and V-de Rham cohomology for an integrable connection with irregular singular points, ibid., 150-153 (1983). · Zbl 0533.32005 · doi:10.3792/pjaa.59.150
[4] Majima, H.: Asymptotic analysis for integrable connections with irregular singular points. (1983) (preprint). · Zbl 0546.58003 · doi:10.1007/BFb0071550
[5] Majima, H. and Sibuya, Y.: Cohomological characterization of regular singularities in several variables. (1984) (preprint).
[6] Malgrange, B.: Ideals of Differentiable Function. Oxford Univ. Press (1966). · Zbl 0177.17902
[7] Ramis, J.-P.: Variation sur le Theme ”GAGA”. Lect. Notes in Math., vol. 694, Springer-Verlag, pp. 228-289 (1978). · Zbl 0398.32008
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