Low-pass filters, martingales, and multiresolution analyses
Necessary and sufficient conditions for a trigonometric polynomial to be a low-pass filter have been given by \textit{A. Cohen} [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 7, No. 5, 439-459 (1990; Zbl 0736.42021)] and \textit{W. M. Lawton} [J. Math. Phys. 31, No. 8, 1898-1901 (1990; Zbl 0708.46020)]. In the paper under review the author gives necessary and sufficient conditions for an arbitrary periodic function to be a low--pass filter, following the approach of Lawton. The technique also applies to functions that give rise to a Riesz basis.
scientific article; zbMATH DE number 1512547
scientific article