Close-to-optimal bounds for loop approximation
The authors continue the investigations of [J. Approx. Theory 161, No. 1, 174--186 (2009; Zbl 1177.22013)] and prove the following result: Let \(N\geq 2\), \(\alpha>1\) and \(\varepsilon>0\). For any \(U(t)\in \text{Lip}_{\alpha}(\mathbb T\rightarrow \text{SU}(N))\), there exists a sequence of \(\text{SU}(N)\)-valued polynomial loops \(U_{n}(t)\) of degree \(\leq n\) such that \[ \|U-U_{n}\|_C\leq C_{\alpha,\varepsilon,N,U}(n+1)^{-(\alpha-\varepsilon)}, \quad n\geq 0. \]
scientific article; zbMATH DE number 5817247
scientific article