Uncertainty products of local periodic wavelets

This paper is on the angle–frequency localization of periodic scaling functions and wavelets. It is shown that the uncertainty products of uniformly local, uniformly regular and uniformly stable scaling functions and wavelets are uniformly bounded from above by a constant. Results for the construction of such scaling functions and wavelets are also obtained. As an illustration, scaling functions and wavelets associated with a family of generalized periodic splines are studied. This family is generated by periodic weighted convolutions, and it includes the well‐known periodic B‐splines and trigonometric B‐splines. This revised version was published online in June 2006 with corrections to the Cover Date.