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Hypoelliptic systems of complex vector fields

H. Maire — 1992

Banach Center Publications

Singular holomorphic functions for which all fibre-integrals are smooth

D. Barlet; H. Maire — 2000

Annales Polonici Mathematici

For a germ (X,0) of normal complex space of dimension n + 1 with an isolated singularity at 0 and a germ f: (X,0) → (ℂ,0) of holomorphic function with df(x) ≤ 0 for x ≤ 0, the fibre-integrals $s \mapsto \int_{f = s} ϱ ω^{'} ⋀ \bar{ω^{''}}, ϱ \in C_{c}^{\infty} (X), ω^{'}, ω^{''} \in Ω_{X}^{n}$ , are $C^{\infty}$ on ℂ* and have an asymptotic expansion at 0. Even when f is singular, it may happen that all these fibre-integrals are $C^{\infty}$ . We study such maps and build a family of examples where also fibre-integrals for $ω^{'}, ω^{''} \in ⍹_{X}$ , the Grothendieck sheaf, are $C^{\infty}$ .

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Currently displaying 1 – 7 of 7

Hypoelliptic systems of complex vector fields

Singular holomorphic functions for which all fibre-integrals are smooth

Régularité optimale des solutions de systèmes différentiels et du Laplacien associé; application au ....b.

Résolubilité et hypoellipticité de systèmes surdéterminés

Existence et régularité des solutions de systèmes différentiels surdéterminés

Sur les Distributions Images Réciproques par une Fonction analytique

Asymptotique des intégrales-fibres