In this paper we present formulas expressing the orthogonal rational functions associated with a rational modification of a positive bounded Borel measure on the unit circle, in terms of the orthogonal rational functions associated with the initial measure. These orthogonal rational functions are assumed to be analytic inside the closed unit disc, but the extension to the case of orthogonal rat...

Yang Shouzhi, Lou Zengjian Department of Mathematics, Shantou University, Shantou 515063, P.R.China Abstract A algorithm is presented for constructing orthogonal multiscaling functions and multiwavelets with multiplicity r+s(s ≥ 1, s ∈ Z) in terms of any given orthogonal multiscaling functions with multiplicity r. That is, let Φ(x) = [φ1(x), φ2(x), · · · , φr(x)] be an orthogonal multiscaling f...