Timeline for Range of Fourier Transform on $L^1$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Jan 16, 2017 at 12:54 | comment | added | user103449 | I agree, but the assumption of being a Shwartz function is a very "strong" assumption (even stronger than "xf(x) integrable") and entails much more that $W^{1,1}$-regularity for the Fourier transform, since it is an isometry on the set of the Schwartz functions. I was rather interested in some kind of "minimal" criterium. Precisely, since I already know that assuming "$xf(x)$ integrable" entails that the Fourier transform is $C^1$, I wondered if there were weaker assumptions under which the Fourier transform would be just $W^{1,1}$. | |
| Jan 12, 2017 at 11:51 | comment | added | user1688 | Yes, many such criteria exist, for instance $f$ being a Schwartz function will do. | |
| Jan 12, 2017 at 11:10 | comment | added | user103449 | I would like to know if there exist (in the literature) sufficient conditions on functions $f\in L^1(\mathbb{R})$ that guarantee that the Fourier transform of $f$ is a function in $W_{loc}^{1,1}(\mathbb{R})$. | |
| Jan 11, 2017 at 11:29 | comment | added | user1688 | Can you make the question more precise? What kind of criteria are you interested in? | |
| Jan 11, 2017 at 10:57 | review | First posts | |||
| Jan 11, 2017 at 10:57 | |||||
| Jan 11, 2017 at 10:53 | history | asked | user103449 | CC BY-SA 3.0 |