Timeline for Upper bound on Lp distance of functions before and after change of variables
Current License: CC BY-SA 4.0
9 events
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| Oct 13, 2019 at 7:03 | comment | added | diadochos | The question arose in statistics. I was wondering how much a distribution function is changed (in its values in the density) by a variable transformation, and I wanted to quantify the change in some measure. The metric did not have to be an Lp-norm, but I thought that would be a good starting point. | |
| Oct 13, 2019 at 7:01 | comment | added | diadochos | Hi, thank you for the quick comments and I'm sorry for the late reply. I understood most of it, but the part saying "the linear map $g \mapsto f_T$" confused me a little. Is it a linear map that maps a D-form to another D-form, instead of $g$ to $f_T$ ? I'll look into the referenced book. Thank you! | |
| Oct 6, 2019 at 18:05 | history | edited | DCM | CC BY-SA 4.0 |
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| Oct 6, 2019 at 17:59 | history | edited | DCM | CC BY-SA 4.0 |
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| Oct 6, 2019 at 16:48 | comment | added | DCM | I hope you'll forgive me for being nosy, but I'd be interested in how you came to ask this question; are you able to give any details of the context in which this question arose? | |
| Oct 6, 2019 at 16:43 | comment | added | DCM | 1. I'm using the word `suitable' here to mean that there exist $\lambda,\Lambda>0$ such that $\lambda < |\mathrm{det}(D\varphi(x))|<\Lambda$ for all $x\in \mathbb{R}^D$. You need this constraint (or at least something like it) to make sure the pullback operation gives you an endomorphism of $X$. | |
| Oct 6, 2019 at 16:42 | history | edited | DCM | CC BY-SA 4.0 |
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| Oct 6, 2019 at 14:55 | history | edited | DCM | CC BY-SA 4.0 |
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| Oct 6, 2019 at 13:58 | history | answered | DCM | CC BY-SA 4.0 |