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Involutivity of truncated microsupports

Masaki Kashiwara, Térésa Monteiro Fernandes, Pierre Schapira (2003)

Bulletin de la Société Mathématique de France

Using a result of J.-M. Bony, we prove the weak involutivity of truncated microsupports. More precisely, given a sheaf F on a real manifold and k ∈ ℤ , if two functions vanish on SS k ( F ) , then so does their Poisson bracket.

Levi's forms of higher codimensional submanifolds

Andrea D'Agnolo, Giuseppe Zampieri (1991)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let X ≅ C n , let M be a C 2 hypersurface of X , S be a C 2 submanifold of M . Denote by L M the Levi form of M at z 0 ∈ S . In a previous paper [3] two numbers s ± ⁢ S , p , p ∈ T ˙ S * ⁢ X z 0 are defined; for S = M they are the numbers of positive and negative eigenvalues for L M . For S ⊂ M , p ∈ S × M T ˙ * S X ) , we show here that s ± ⁢ S , p are still the numbers of positive and negative eigenvalues for L M when restricted to T z 0 C ⁢ S . Applications to the concentration in degree for microfunctions at the boundary are given.

On the C ∞ -singularities of regular holonomic distributions

Emmanuel Andronikof (1992)

Annales de l'institut Fourier

The analytic and 𝒞 ∞ wave-front sets of a distribution which is a solution of a regular holonomic differential system are shown to coincide. More generally, we give comparison theorems for solutions of a regular holonomic system of microdifferential equations in various spaces of microfunctions, as a simple extension of a result of Kashiwara.

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