Affine synthesis onto $L^p$ when $0 < p \leq 1$

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dc.creatorLaugesen, R. S.
dc.date2007-03-11
dc.date.accessioned2026-07-07T07:51:26Z
dc.date.available2026-07-07T07:51:26Z
dc.descriptionThe 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 $p>1$.
dc.description29 pages
dc.identifierhttps://arxiv.org/abs/math/0703313
dc.identifierhttp://arxiv.org/abs/math/0703313
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125510
dc.subjectClassical Analysis and ODEs
dc.subject41A30; 46E30
dc.titleAffine synthesis onto $L^p$ when $0 < p \leq 1$
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