Reparametrization invariant norms
| dc.creator | Frosini, Patrizio | |
| dc.creator | Landi, Claudia | |
| dc.date | 2007-02-05 | |
| dc.date.accessioned | 2026-07-07T07:44:48Z | |
| dc.date.available | 2026-07-07T07:44:48Z | |
| dc.description | This paper explores the concept of reparametrization invariant norm (RPI-norm), that is any norm invariant under composition with diffeomorphisms. We prove the existence of an infinite family of RPI-norms, called standard RPI-norms, for which we exhibit both an integral and a discrete characterization. Our main result states that, for every one-time differentiable piecewise monotone function with compact support, its standard RPI-norms allow us to compute the value of any other RPI-norm of the same function. This is proved by using the standard RPI-norms in order to reconstruct the function up to reparametrization and an arbitrarily small error with respect to the total variation norm. | |
| dc.description | 50 pages, 10 figures | |
| dc.identifier | https://arxiv.org/abs/math/0702094 | |
| dc.identifier | http://arxiv.org/abs/math/0702094 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123332 | |
| dc.subject | Functional Analysis | |
| dc.subject | 46E10; 46B20 | |
| dc.title | Reparametrization invariant norms | |
| dc.type | text |