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Diffraction analytique sur une variété à singularité conique. (Analytic diffraction on a manifold with conic singularity). (English) Zbl 0698.58049
The author establishes some results that he announced in C. R. Acad. Sci., Paris, Sér. I 300, 1-4 (1985; Zbl 0584.58043) on the analytic regularity of the kernel of the fundamental solution of the wave equation on a manifold with conic singularity, with Dirichlet condition.
After specifying in Section I the results of J. Cheeger and M. Taylor about the decomposition of the kernel of the fundamental solution [Commun. Pure Appl. Math. 25, 275-331 (1982; Zbl 0526.58049)], especially on the existence and uniqueness of the Cauchy problem in some Sobolev spaces and recalling the construction of the kernel, the author studies in Section II the analytic continuation of the eigenfunctions of the Laplacian. In Section III he assembles these results to derive the analytic regularity of the kernel ‘behind the diffracted wave front’.

MSC:
58J45 Hyperbolic equations on manifolds
35P99 Spectral theory and eigenvalue problems for partial differential equations
35L05 Wave equation
35S05 Pseudodifferential operators as generalizations of partial differential operators
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