Timeline for Decompose a function into a bounded part and a Lipschitz part
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 28 at 19:24 | comment | added | Terry Tao | Another approach (relying not on discretization, but on the vector space structure on ${\bf R}^d$) is to take $g$ to be a convolution of $f$ with a standard bump function of unit mass. Verifying the required estimates is then a nice undergraduate real analysis exercise. | |
| Feb 27 at 16:18 | comment | added | Nik Weaver | Yeah, good point. | |
| Feb 27 at 16:05 | comment | added | Terry Tao | One does not even need triangulation, since any scalar Lipschitz function on a subset of a metric space can be extended to a Lipschitz function on the full space with the same Lipschitz constant. Since the restriction of $f$ to say ${\bf Z}^d$ is already Lipschitz, just extend each component to get $g$. (Presumably the general theory of quasi-isometries would also handle this question, though I didn't see a particularly slick way to do so.) | |
| Feb 27 at 13:30 | vote | accept | Akira | ||
| Feb 27 at 13:14 | history | answered | Nik Weaver | CC BY-SA 4.0 |