This 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.
Selected lectures in microlocal analysis
ZAMPIERI, GIUSEPPE
2009
Abstract
This 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.
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