Trigonometric rational wavelet bases (Q2781639)

A construction of periodic rational bases of wavelets is proposed. The relevant Multiresolution Analysis (MRA) possesses the following properties. 1) the MRA consists of rational trigonometric functions; 2) the uniform limit function of the sequence of periodic interpolating scaling functions \(\varphi^n (2^{-n} x)\) is the Shannon scaling function; 3) the corresponding limit function for the Fourier transform \(\widehat \varphi^n (2^{n} \omega)\) is a Riemann-like function which is discontinuous at binary-rational points and continuous at the remaining points. This construction is well motivated.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00015].