Timeline for Are Besov spaces $B^{s}_{p,q}$ invariant under Fourier transform?
Current License: CC BY-SA 3.0
12 events
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| S Oct 3, 2014 at 12:37 | history | suggested | CommunityBot | CC BY-SA 3.0 |
Corrected minor grammar and spelling issue in title.
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| Oct 3, 2014 at 12:12 | review | Suggested edits | |||
| S Oct 3, 2014 at 12:37 | |||||
| Sep 4, 2014 at 13:13 | answer | added | Bazin | timeline score: 6 | |
| Sep 2, 2014 at 15:24 | comment | added | Inquisitive | @CPJ; your link is indeed useful; thanks | |
| Sep 2, 2014 at 15:21 | comment | added | Inquisitive | @CPJ;thanks; but still I wonder how is that true ? (Because bit roughly speaking, dyadic decomposition operators combined with function spaces $\ell^{q}(L^{p})$ generate Besov spaces, frequency-uniform decomposition operators joint with function spaces $\ell^{q}(L^{p})$ produce modulation spaces. ) I have been trying to seek the underneath crucial point..; thanks | |
| Sep 2, 2014 at 15:05 | comment | added | CPJ | I think Besov spaces do not contain spaces that are invariant under the Fourier transform. That is at least what Feichtinger says in univie.ac.at/nuhag-php/bibtex/open_files/fe83-1_mod-kiev.pdf and I sort of trust him on this. See page 5. | |
| Sep 2, 2014 at 13:55 | comment | added | CPJ | As I said I don't know whether or not the Fourier pictures of Besov spaces are Besov spaces; I think in genral it is not the case. (I think the reason for the introduction of modulation spaces was exactly this question to find Fourier-invariant spaces. univie.ac.at/nuhag-php/bibtex/open_files/…) | |
| Sep 2, 2014 at 12:53 | comment | added | Inquisitive | @CPJ; Thanks, but $M^{1,1}\subset B^{0}_{1,1}$; so I don't know how does it help here ?; thanks | |
| Sep 2, 2014 at 12:37 | comment | added | CPJ | What do you mean by "(5) Is there some thing special about dyadic decompositions?" Since some Besov spaces can be embedded in modulation spaces you could write their norms with frequency uniform decompositions. Like $B^s_{2,2} = M_{2,2}^s$ coincides with $H^{s}$ so it is characterizable by dyadic or frequency uniform decompositions. | |
| Sep 2, 2014 at 12:25 | comment | added | CPJ | I know that the Fourier transform of a function in a modulation space is at least again in a modulation space. Depending a bit on their definition, the usual 3 parameter definition should be invariant?! I think for $p=q$. | |
| Sep 2, 2014 at 11:56 | history | edited | Inquisitive | CC BY-SA 3.0 |
added 3 characters in body
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| Sep 2, 2014 at 11:50 | history | asked | Inquisitive | CC BY-SA 3.0 |