Timeline for Proving that a function $f(x,y)$, that is unbounded in every direction, is uniformly bounded below by $1$ outside some disc of large enough radius
Current License: CC BY-SA 4.0
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| Jul 18 at 20:48 | comment | added | Ryan Hendricks | I have now asked a follow up question, with the additional restriction that $f(x,y)$ is a polynomial- mathoverflow.net/questions/475327/… | |
| Jul 18 at 18:21 | comment | added | Iosif Pinelis | @RyanHendricks : Right. The smooth counterexample is just a modification of the non-smooth one. | |
| Jul 18 at 17:53 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jul 18 at 17:48 | vote | accept | Ryan Hendricks | ||
| Jul 18 at 17:44 | comment | added | Ryan Hendricks | Thank you. I suppose the basic idea behind the smooth example is that for points where $x^2 y^2$ is small, but $(x^2+y^2)$ is large enough to ensure that $(x^2+y^2)e^{-x^2 y^2(x^2+y^2)}$ is effectively $0$, the function is equal to $x^2 y^2$, and is hence small? | |
| Jul 18 at 17:37 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jul 18 at 17:27 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jul 18 at 17:16 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |