Higher P-symmetric Ekeland-Hofer capacities

<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>