Microlocal kernel of pseudodifferential operators at a hyperbolic fixed point
نویسندگان
چکیده
منابع مشابه
Microlocal Kernel of Pseudodifferential Operators at an Hyperbolic Fixed Point Jean-françois Bony, Setsuro Fujiie, Thierry Ramond, and Maher Zerzeri
We study the microlocal kernel of h-pseudodifferential operators Oph(p) − z, where z belongs to some neighborhood of size O(h) of a critical value of its principal symbol p0(x, ξ). We suppose that this critical value corresponds to a hyperbolic fixed point of the Hamiltonian flow Hp0 . First we describe propagation of singularities at such a hyperbolic fixed point, both in the analytic and in t...
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The study of pseudodifferential operators emerged in the 1960’s, having its origins in the study of singular integro-differential operators. In fact, Friedrichs and Lax coined the term “pseudodifferential operator” in their 1965 paper entitled “Boundary Value Problems for First Order Operators”. Since that time, pseudodifferential operators have proved useful in many arenas of modern analysis a...
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We introduce new Lagrangian cycles which encode local contributions of Lefschetz numbers of constructible sheaves into geometric objects. We study their functorial properties and apply them to Lefschetz fixed point formulas with higherdimensional fixed point sets.
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The authors develop a calculus of pseudodifferential operators with nonsmooth coefficients in order to study the regularity of solutions to linear equations P(x, D)u = /. The regularity theorems are similar to those of Bony, but the calculus and the methods of proof are quite different. We apply the linear results to study the regularity properties of solutions to quasilinear partial differenti...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2007
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2007.07.003