This question is related to the signatures that arises in rough path theory. https://en.wikipedia.org/wiki/Rough_path
Is there any reference to understand if the norms of the different levels of signatures are convex function or not? is it possible to derive under what condition the norm (L1 or L2) of the first or second level of signature would be convex? As I understand L1 and L2 norm are convex by definition, but is that applicable to the first and second level of signature. The Gemini the language model says no so I am confused.