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Session 17. Functional Analysis: relations to Complex Analysis and PDE
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Wave front sets with respect to the iterates of an operator with constant coefficients
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David Jornet, Universitat Politècnica de València,
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The talk is based on the joint work with Chiara Boiti and Jordi Juan-Huguet
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We introduce the wave front set \(WF^P_\ast(u)\) with respect to the iterates of a hypoelliptic linear partial differential operator with constant coefficients of a classical distribution \(u\in\mathcal{D}'(\Omega)\) in an open set \(\Omega\) in the setting of ultradifferentiable classes of Braun, Meise and Taylor. We state a version of the microlocal regularity theorem of Hörmander [2, Theorem 5.4] for this new type of wave front set and give some examples and applications of the former result.
This talk is based on the recently published paper [1].
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References- C. Boiti, D. Jornet, J. Juan-Huguet, Wave front sets with respect to the iterates of an operator with constant coefficients , Abstr. Appl. Anal. Volume 2014 (2014), Article ID 438716, 17 pages, http://dx.doi.org/10.1155/2014/438716
- L. Hörmander, Uniqueness theorems
and wave front sets for solutions of linear partial differential equations
with analytic coefficients , Comm. Pure Appl. Math. 24 (1971), 671-704.
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