Which RPI-norms are the supremum of standard RPI-norms?

Baggio, Silvano (2008) Which RPI-norms are the supremum of standard RPI-norms? [Preprint]
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We settle some open problems regarding RPI-norms, i.e. norms (on a convenient subspace of differentiable real functions) that are invariant under differentiable reparametrizations. More precisely, we clarify some key points on how RPI-norms can be approximated using standard RPI-norms. We first prove that the sum of two standard RPI-norms is the supremum of a set of standard RPI-norms. This allows us to study a class of RPI-norms that can be expressed as the sup of standard ones. Finally, we give a positive answer to an open question on the existence of RPI-norms that are not the sup of standard RPI-norms.

Document type
Baggio, Silvano
invariant norms, differentiable reparametrizations
Deposit date
04 Mar 2008
Last modified
16 May 2011 12:07

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