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- W2951574756 abstract "If $varphi$ and $psi$ are two continuous real-valued functions defined on a compact topological space $X$ and $G$ is a subgroup of the group of all homeomorphisms of $X$ onto itself, the natural pseudo-distance $d_G(varphi,psi)$ is defined as the infimum of $mathcal{L}(g)=|varphi-psi circ g |_infty$, as $g$ varies in $G$. In this paper, we make a first step towards extending the study of this concept to the case of Lie groups, by assuming $X=G=S^1$. In particular, we study the set of the optimal homeomorphisms for $d_G$, i.e. the elements $rho_alpha$ of $S^1$ such that $mathcal{L}(rho_alpha)$ is equal to $d_G(varphi,psi)$. As our main results, we give conditions that a homeomorphism has to meet in order to be optimal, and we prove that the set of the optimal homeomorphisms is finite under suitable conditions." @default.
- W2951574756 created "2019-06-27" @default.
- W2951574756 creator A5004309997 @default.
- W2951574756 date "2017-03-04" @default.
- W2951574756 modified "2023-09-27" @default.
- W2951574756 title "On the set of optimal homeomorphisms for the natural pseudo-distance associated with the Lie group S^1" @default.
- W2951574756 hasPublicationYear "2017" @default.
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