1,721,055 research outputs found
The Andreotti Grauert vanishing theorem for dihedrons of C\sp n
No full textLet be a complex manifold, \OX the sheaf of analytic functions on , an open set of with -boundary ( locally on one side of ), a point of , the exterior conormal to at . If the number of negative eigenvalues for the Levi form of in a neighborhood of is (resp. ), then vanishing of local cohomology groups of \OX over in degree
Selected lectures in microlocal analysis
No full textThis paper is a survey of some classical results on microlocal analysis. The first part recalls in particular the notion of analytic wave front set and the theorem of elliptic regularity, along the lines of [M. Sato, T. Kawai and M. Kashiwara, in Hyperfunctions and pseudo-differential equations, 265--529, Lecture Notes in Math., 287, Springer, Berlin, 1973; MR0420735 (54 #8747)] and [L. V. Hörmander, The analysis of linear partial differential operators. I, Grundlehren Math. Wiss., 256, Springer, Berlin, 1983; MR0717035 (85g:35002a)]. The second part deals with propagation of microlocal singularities. It starts with the classical Holmgren uniqueness theorem and proceeds to discuss some variations thereof on propagation at the boundary, where the author has made several contributions
Reflection about -jets and holomorphic extension of CR mappings
No full textAbstractLet f:M→M1 be a CR mapping between real analytic generic submanifolds M, M1 of CN and CN1, respectively. According to Webster's theory (Proc. Amer. Math. Soc. 86 (1982) 236–240) and its further developments, f has holomorphic extension to a full neighborhood of M in CN when the following requirements are fulfilled: f extends to a wedge W continuous up to M; f is of class Ck; f′TCM=TCM1 (where TC denotes the complex tangent bundle); M1 is “k-nondegenerate.” We deal here with the case where f′TCM is strictly smaller than TCM1 but is still real analytic in suitable sense. We show that a suitably refined condition of k-nondegeneracy still entails holomorphic extension of f
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