Construction of \(\alpha\)-Hölderian wavelets basis (Q1175970)

The author recovers an Ingrid Daubechis method to generate orthonormal function basis in \(L^ 2(\mathbb{R})\) of the form \(\{2^{1/2}\psi(2^ j x-k)\}\), \(j,k\in\mathbb{Z}\), using quadrature mirror filters (QMF), so that the wavelet (ondelette) \(\psi\) have good regularity properties. An estimation of the global optimal Hölder exponent that characterize the decreasing of the function \(\hat\psi\) is obtained. Finally the exact relation among the wavelet regularity and his cancellation order, is precised.