Wavelets of Wilson type with arbitrary shapes

Motivated by the Gaussian bases of Coifman and Meyer and the need of bases with arbitrary shapes which may have to be different at different locations , we derive complete characterizations of window functions and their duals for localization of all appropriate sines and cosines that give rise to bio rthogonal Schauder bases, Riesz bases, and frames. In addition, when the wi ndow functions are simply integer translates of a single window function, w e give an explicit formulation of its dual that generates the biorthogonal basis, regardless of the shape and support of the window function. Besides the Coifman-Meyer Gaussian bases, several other examples of wavelets of Wil son type are given. (C) 2000 Academic Press.