On the unconditional convergence of wavelet expansions for continuous functions (Q2800848)

The convergence of wavelet series depending on the ordering of the wavelet coefficients is analyzed. For Lipschitz continuous wavelets it is shown that there exist functions having some particular regularity, for which the wavelet series converges uniformly in \(L^\infty\), but not unconditionally.NEWLINENEWLINENEWLINEThe authors use the Strömberg wavelets, which have exponential decay and for which the exact values at the nodes are known. A construction of a continuous function is given whose wavelet series converges uniformly and non-unconditionally in \(L^\infty\).