Symbols and exact regularity of symmetric pseudo-splines of any arity

Using a generating function approach, we derive expressions for the symbols of the symmetric m-ary pseudo-spline subdivision schemes. We show that their masks have a positive (discrete-time) Fourier transform, making it possible to compute the exact Hölder regularity algebraically as the spectral radius of a matrix. We apply this method to compute the regularity explicitly in some special cases, such as the symmetric binary and ternary pseudo-spline schemes.