Symbols and exact regularity of symmetric pseudo-splines of any arity (Q2411655)

In the paper under review, the subdivision framework is considered (recursive methods for generating geometric objects), one family of subdivision scheme being pseudo-splines, a natural blend between interpolating schemes and approximating schemes, including Dubuc-Deslauriers schemes and B-splines schemes. The authors first define the \(m\)-ary pseudo-splines and then derive their symbols as a truncated generating function, Their regularity are analyzed. It is shown that their masks have positive Fourier transform making it possible to compute the exact Holder regularity algebraically as a logarithm of the spectral radius of a matrix. The method is used to compute regularity in some special cases, as symmetric binary, ternary, quarternary pseudo-spline schemes.