Denjoy-Carleman Microlocal Regularity on Smooth Real Submanifolds of Complex Space

Antonio Victor da Silva Jr.; Nicholas Braun Rodrigues

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arXiv · 2207.12017

Denjoy-Carleman Microlocal Regularity on Smooth Real Submanifolds of Complex Space

Antonio Victor da Silva Jr.·Nicholas Braun Rodrigues

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Abstract

We prove the existence of approximate solutions in the (regular) Denjoy-Carleman sense for some systems of smooth complex vector fields. Such approximate solutions provide a well defined notion of Denjoy-Carleman wave front set of distributions on maximally real submanifolds in complex space which can be characterized in terms of the decay of the Fourier-Bros-Iagolnitzer transform. We also apply the approximate solutions to analyze the Denjoy-Carleman microlocal regularity of solutions of certain systems of first-order nonlinear partial differential equations.

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Antonio Victor da Silva Jr., Nicholas Braun Rodrigues. 2022-07-25. Denjoy-Carleman Microlocal Regularity on Smooth Real Submanifolds of Complex Space. https://arxiv.org/abs/2207.12017

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