Talk:Legendre transformation

Possible copyright problem
The exposition quite closely follows the reference Rockafellar. I hope this is not a copyright problem. &mdash;the preceding unsigned comment is by 84.239.128.9 (talk &bull; contribs) 09:26, 31 October 2005 (UTC1)

Name for this property?
Does anybody know how the property

f(x_1, \dots, x_N) = g(x_1) + \cdots + g(x_N) \; \Rightarrow \; f^\star(p_1, \dots, p_N) = g^\star(p_1) + \cdots + g^\star(p_N) $$ is refered to in the literature? &mdash;the preceding unsigned comment is by Tobias Bergemann (talk &bull; contribs) 12:12, 13 December 2005 (UTC1)

$$x^* \rightarrow \varphi$$ for clarity
In the definition, I would switch the $$x^*$$ to $$\varphi$$ (or something else) for clarity. Hvstms (talk) 10:48, 19 September 2023 (UTC)

Circularity in definition
The definitions provided are phrased in a confusing way, with the domain of the function $$f_*$$ depending on $$f_*$$ itself. One can avoid this by saying, for example, 'defined where this supremum is finite', or simply by repeating the function's definition in the definition for $$I_*$$, ie $$I_* = \{y \in \mathbb{R} : \sup_{x \in \mathbb{R}}\{ xy - f(x)\} < \infty\}$$. Happy to make this edit myself if others agree, but this is not my area of expertise and if this circularity is common in related texts and papers it probably makes sense to keep it here. Corlio5994 (talk) 06:16, 16 March 2024 (UTC)