In this paper, we give some estimations for Ekeland-Hofer-Zehnder capacities of lagrangian products with special forms through combinatorial formulas. Based on these estimations, we give some interesting corollaries.
This paper is devoted to the construction of analogues of higher Ekeland-Hofer symplectic capacities for P -symmetric subsets in the standard symplectic space (R 2n , ω 0 ), which is motivated by Long and Dong's study P -symmetric closed characteristics on P -symmetric convex bodies. We study the relationship between these capacities and other capacities, and give some computation examples. Moreover, we also define higher real symmetric Ekeland-Hofer capacities as a complement of Jin and the second named author's recent study of the real symmetric analogue about the first Ekeland-Hofer capacity.
<p style='text-indent:20px;'>This paper is devoted to the construction of analogues of higher Ekeland-Hofer symplectic capacities for <inline-formula><tex-math id="M2">\begin{document}$ P $\end{document}</tex-math></inline-formula>-symmetric subsets in the standard symplectic space <inline-formula><tex-math id="M3">\begin{document}$ (\mathbb{R}^{2n},\omega_0) $\end{document}</tex-math></inline-formula>, which is motivated by Long and Dong's study about <inline-formula><tex-math id="M4">\begin{document}$ P $\end{document}</tex-math></inline-formula>-symmetric closed characteristics on <inline-formula><tex-math id="M5">\begin{document}$ P $\end{document}</tex-math></inline-formula>-symmetric convex bodies. We study the relationship between these capacities and other capacities, and give some computation examples. Moreover, we also define higher real symmetric Ekeland-Hofer capacities as a complement of Jin and the second named author's recent study of the real symmetric analogue about the first Ekeland-Hofer capacity.</p>
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