Abstract
This paper is devoted to function theory on symplectic manifolds. We study a natural class of functionals involving the double Poisson brackets from the viewpoint of their robustness properties with respect to small perturbations in the uniform norm. We observe a hierarchy of such robustness properties. The methods involve Hofer's geometry on the symplectic side and Landau-Hadamard- Kolmogorov inequalities on the function-theoretic side.
Original language | English |
---|---|
Pages (from-to) | 1134-1158 |
Number of pages | 25 |
Journal | International Mathematics Research Notices |
Volume | 2009 |
Issue number | 6 |
DOIs | |
State | Published - 2009 |
ASJC Scopus subject areas
- General Mathematics