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Results tagged with convex-analysis
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user 113397
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A function with unexpectedly simple Legendre transformation
Claim. $J(x)=\tfrac12x^2+\ln|x|+c$ for $|x|>1$ with $c$ constant.
Proof: Here, an explicit form for $I(x)$ is not needed but I can't use it to prove $c=0$.
For $|x|>1$, the substitution $y=2\cos t$ fo …
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