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A propagation theorem for a class of microfunctions

Andrea D'Agnolo, Giuseppe Zampieri (1990)

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

Let A be a closed set of M R n , whose conormai cones x + y x * A , x A , have locally empty intersection. We first show in §1 that dist x , A , x M A is a C 1 function. We then represent the n microfunctions of C A | X , X C n , using cohomology groups of O X of degree 1. By the results of § 1-3, we are able to prove in §4 that the sections of C A | X π ˙ - 1 x 0 , x 0 A , satisfy the principle of the analytic continuation in the complex integral manifolds of H ϕ i C i = 1 , , m , ϕ i being a base for the linear hull of γ x 0 * A in T x 0 * M ; in particular we get Γ A × M T * M X C A | X A × M T ˙ * M X = 0 . When A is a half space with C ω -boundary,...

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