Totally positive functions through nonstationary subdivision schemes (Q859886)

The goal of the paper is to use nonstationary subdivision schemes for constructing symmetric and totally positive functions having the same support but higher smoothness than B-splines. In particular, the authors construct totally positive symmetric functions with support of length \( n \) and smoothness \(C^{n-1}. \) It is shown that the constructed nonstationary subdivision schemes are asymptotically equivalent to the stationary subdivision schemes associated with a B-spline of suitable degree.