We investigate the effects of the δ 2 transform on the partial sums of Fourier series for functions with a finite number of jumps, which in general, converge slowly. Although the δ 2 process is known to accelerate convergence for many sequences, we prove that in this case, the transformed series will usually fail to converge to the original function.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.