Timeline for Are there examples of functions in $L_1$ and $L_\infty$ whose Fourier series divergent ("weakly")?
Current License: CC BY-SA 3.0
8 events
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| May 20, 2015 at 17:10 | vote | accept | user228494 | ||
| May 20, 2015 at 12:57 | comment | added | Gerald Edgar | @user228494: Uniform boundedness principle. An interesting method to show existence. But your question asks for "some examples" and UBP is not the way to produce explicit examples. | |
| May 20, 2015 at 8:31 | comment | added | user228494 | Thanks! But I also can't understand why does Uniform Boundedness Principle implies divergence of Fourier series in $L_\infty$, I have read it somewhere, but it seems not to be so obvious for me | |
| May 20, 2015 at 5:25 | history | edited | Robert Israel | CC BY-SA 3.0 |
added 200 characters in body
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| May 20, 2015 at 0:21 | comment | added | Robert Israel | As $x \to 0$, $\ln(1-\cos(x)) \sim 2\ln|x|$, which is an integrable singularity. | |
| May 19, 2015 at 21:31 | vote | accept | user228494 | ||
| May 19, 2015 at 21:32 | |||||
| May 19, 2015 at 20:45 | comment | added | user228494 | But why $ln(1-cos(x))$ is in $L_1$, why is it integrable? | |
| May 19, 2015 at 20:13 | history | answered | Robert Israel | CC BY-SA 3.0 |