Topological Obstructions to Localization Results

In this paper we present topology aspects in non-localization results. A well-known such no-go result is the BalianLow theorem that states the generator of a Weyl-Heisenberg Riesz basis cannot be well time-frequency localized. More general, the statement applies to multi WH Riesz bases, or super frames as well. These results turn out to be connected to non-triviality of a complex vector bundle. Another class of problem is related to optimality of coherent approximations of stochastic signals. More speci c, for a given de cit ( > 1), nd the best Riesz sequence generator optimal to respect to the mean square approximation error. A topological obstruction turns out to be responsable for ill-localization of the optimal generator.