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Quasi-states and the Poisson bracket on surfaces

Frol Zapolsky
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Abstract

We present a convexity-type result concerning simple quasi-states on closed manifolds. As a corollary, an inequality emerges which relates the Poisson bracket and the measure of non-additivity of a simple quasi-state on a closed surface equipped with an area form. In addition, we prove that the uniform norm of the Poisson bracket of two functions on a surface is stable from below under C^0-perturbations.

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Frol Zapolsky. 2007-03-05. Quasi-states and the Poisson bracket on surfaces. https://arxiv.org/abs/math/0703121

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