Rouleux, M. Diffraction analytique sur une variété à singularité conique. (Analytic diffraction on a manifold with conic singularity). (English) Zbl 0698.58049 Commun. Partial Differ. Equations 11, No. 9, 947-988 (1986). 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’. Cited in 8 Documents 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 Keywords:analytic regularity of the wave-kernel; manifold with conic singularity; eigenfunctions of the Laplacian Citations:Zbl 0584.58043; Zbl 0526.58049 PDFBibTeX XMLCite \textit{M. Rouleux}, Commun. Partial Differ. Equations 11, 947--988 (1986; Zbl 0698.58049) Full Text: DOI References: [1] Baouendi et M.S., Rev. Roum Math. Pures et Appl., XVIII, n{\(\deg\)} 10, Bucarest pp 1495– (1973) [2] Battet de monvel L., Comptes Rendus, 287 pp 855– (1978) [3] Cheeger et J., C.P.A.M. pp 275– (1982) [4] Lebedev N., Indiana University Math. J., 30 pp 389– (1981) · Zbl 0424.35003 [5] Rouleux M., Comptes Rendus. 300 pp 1– (1985) [6] Sjöstrand J., Astérisque 95 (1985) [7] Titchmarsch E.C., Proc. Cambridge Phil. SOC. 21 pp 947– (1923) [8] Treves F., Notas de Matem. 46 (1968) [9] Watson G., A treatise on the theory of Bessel functions (1966) · Zbl 0174.36202 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.