Uniqueness in the Cauchy Problem for Singular Principally Normal Operators
speaker: Daniele Del Santo (Università di Trieste, Dipartimento di Matematica e Geoscienze)abstract: The course has been devoted to present some results on uniqueness in the Cauchy problem for singular principally normal operators. The first part of the course concerned some classical topics, mainly the technique of Carleman estimates and the Hoermander's theorem on uniqueness in the Cauchy problem for principally normal operators when the initial surface is strongly pseudoconvex. The proof of the latter result has been given stressing the fact that the crucial point is the Fefferman-Phong inequality. In the second part of the course the attention was tourned on some possible generalizations of the recalled Hoermander's result. In particular the use of singular weights in Carleman estimates leads to the definition of singular principally normal operators. These operators have the compact uniqueness in the Cauchy problem when the characteristics roots are simple. The main point in the proof is again a Fefferman-Phong type estimate which holds in locally tempered Weyl Calculus.
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