On a family of filters arising in wavelet construction

Wavelet reconstruction almost always reduces to the study of certain algebraic identities for polynomials. Typically, one polynomial is chosen and another is found which satisfies an identity appropriate for the desired wavelet construction. In this paper we explore one such equation and give applications of it to wavelet construction. The specific equation we study here comes to us from our recent work on iterative interpolation by exponentials. Through this equation we strive to unify several related questions concerning wavelet construction and provide in each case considered estimates for the decay of the Fourier transform of both the refinable functions and corresponding wavelets. © 1997 Academic Press.