ABSTRACT
The only available initial building block for the theoretical and algorithmic development of wavelet subdivision methods (for parametric curves) is a finitely supported sequence that satisfies the sum-rule condition of order greater than or equal to 2. To develop a unified theory that also applies to the construction of synthesis wavelets associated with the interpolatory scaling functions, this chapter considers a more general polynomial and studies a class of algebraic polynomial identities. A fundamental theorem of existence and uniqueness is established, with a constructive proof that also yields an algorithm for constructing the minimum-degree polynomial solution.
