Moreover, it implies that every function in (H^{s}) has a unique expansion in the scaled wavelet basis and that there is a tight relation between the function norms and wavelet coefficients.
If Ψ is a Schauder basis of a Banach space X, then for any (xin X) there exists a unique expansion x=sum_{i=1}^{infty}e_{i}^(x e_{i}, which means the partial sum sequence ({S_{m}(x)}) defined in (2.1) converges to x in X norm for every (xin X).
Last summer, the Bureau of Land Management (BLM) announced a unique "expansion" with Border Patrol in the federal deployment of prison inmate-trained horses to the already heavily militarized US/Mexico border.
Prior to the 1991-92 season, the Sharks and North Stars participated in a unique expansion draft, which saw San Jose select unprotected players from Minnesota (including future All-Star goalie Arturs Irbe) before both teams picked players from the remainder of the league.
It is apparent that fleas achieved a unique expansion of acid phosphatases, at least nine members of which were identified in the salivary glands using MS/MS.
The fintrim genes constitute a unique expansion of trim genes in different teleost species, with up to 84 genes identified in zebrafish (Danio rerio).
