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

R. S. Laugesen

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

R. S. Laugesen

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Abstract

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 $p>1$.

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BibTeX RIS

R. S. Laugesen. 2007-03-11. Affine synthesis onto $L^p$ when $0 < p \leq 1$. https://arxiv.org/abs/math/0703313

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