I need to find an orthonormal basis of $H^2(-N,N)$ where $N \in \mathbb{N}$ and $H^2$ denotes the Sobolev space $W^2_2$. I have no idea how to start. A hint to some literatur would be perfect.
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1Please see http://math.stackexchange.com/questions/214441/orthonormal-basis-for-sobolev-spaces – anonymous Feb 15 '13 at 21:09
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Does http://dx.doi.org/10.1007/s10625-005-0195-1 help? – anonymous Feb 15 '13 at 21:16
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@anonymous Not really. That are more complicated spaces and there is no (closed form)-basis given – mjb Feb 22 '13 at 13:28
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What is the norm for which the basis should be orthonormal? – ˈjuː.zɚ79365 Jun 07 '13 at 12:12
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$\Vert v \Vert_{H^2}^2 = \Vert v \Vert_{L^2}^2 + \Vert Dv \Vert_{L^2}^2 + \Vert D^2v \Vert_{L^2}^2$ – mjb Aug 22 '13 at 13:44