Time-frequency concentration of generating systems

Uncertainty principles for generating systems ${e_n}_{n=1}^{\infty} \subset \ltwo$areprovenandquantifytheinterplaybetween$\ell^r(\N)$ coefficient stability properties and time-frequency localization with respect to $\mathrm{\mid }t{\mathrm{\mid }}^p$ power weight dispersions. As a sample result, it is proven that if the unit-norm system $\{e_n{\}}_{n=1}^{\mathrm{\infty }}$ is a Schauder basis or frame for $\text{ltwo}$ then the two dispersion sequences $\mathrm{\Delta }(e_n)$, $\mathrm{\Delta }(\overline{e_n})$ and the one mean sequence $\mu (e_n)$ cannot all be bounded. On the other hand, it is constructively proven that there exists a unit-norm exact system $\{f_n{\}}_{n=1}^{\mathrm{\infty }}$ in $\text{ltwo}$ for which all four of the sequences $\mathrm{\Delta }(f_n)$, $\mathrm{\Delta }(\overline{f_n})$, $\mu (f_n)$, $\mu (\overline{f_n})$ are bounded.