Affine synthesis onto $L^p$ when $0 < p \leq 1$
Abstract
Description
The affine synthesis operator is shown to map the coefficient space $\ell^p$ surjectively onto $L^p$, for $0 < p \leq 1$. Here the synthesizer need satisfy only mild restrictions, for example having nonzero integral or else periodization that is real-valued, nontrivial and bounded below.
Consequences include an affine atomic decomposition of $L^p$.
Tools include an analysis operator that acts nonlinearly, in contrast to the usual linear analysis operator for $p>1$.
29 pages
29 pages