GENERAL PERIODIC FRANKLIN SYSTEM AS A BASIS IN H~1 [0,1]

摘要

The general periodic Franklin system corresponding to a sequence of knots T = {t_n, n ≥ 0} dense in [0,1] is defined to be a sequence of orthonormal, piecewise linear, continuous functions f_n(x) with knots T satisfying f_n(0) = f_n(1). The main result of this paper yields a characterization of those sequences T, for which the corresponding general periodic Franklin system is a basis or an unconditional basis in H~1[0,1].