I'm studyind Majda Bertozzi book about vorticity and incompressible flow, and I don't know what's the 0 norm which appears in it. Thanks a lot!
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Sometimes $\lVert x\rVert_0=\lvert\lbrace k,:, x_k\ne 0\rbrace\rvert$, so for instance $\lVert (1,0,-5,3)\rVert_0=3$. – Sep 08 '18 at 09:31
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As the first line of p. 89 says, $\|\cdot\|_0$ is the $L^2$ norm on $\mathbb{R}^N$. The $0$ makes sense when you check out p. 97, where this is generalised to Sobolev spaces of functions having derivatives up to order $m$ that are in $L^2$. $L^2$ is then the case $m=0$.
Kusma
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