Orthogonal trigonometric Schauder bases of optimal degree for \(C(K)\) (Q1907300)

Applying the idea of gray coding to wavelet packets derived from trigonometric wavelets, the authors constructed an orthonormal Schauder basis of \(C(|z|= 1)\) with ``minimal'' degrees. Here, minimality means that for each \(\varepsilon> 0\), the \(n\)th trigonometric polynomial in this construction is of degree \(\leq {1\over 2}(1+ \varepsilon)n\). It is a well-known result of Faber that \(\varepsilon\) cannot be replaced by \(0\).