Timeline for Besicovitch Almost Periodic Functions a subspace of what?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Mar 5, 2014 at 17:39 | vote | accept | Greg Zitelli | ||
| Mar 4, 2014 at 19:48 | comment | added | Delio Mugnolo | also, I would refrain from calling this the common example of a nonseparable Hilbert space. | |
| Mar 3, 2014 at 14:52 | comment | added | Gerald Edgar | If it is, in fact, incomplete, I think that would answer your question. | |
| Mar 2, 2014 at 20:05 | answer | added | Gerald Edgar | timeline score: 4 | |
| Mar 2, 2014 at 20:00 | history | edited | Greg Zitelli | CC BY-SA 3.0 |
added 21 characters in body
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| Mar 2, 2014 at 19:59 | comment | added | Greg Zitelli | The definition is careless. Although relying solely on a supremum might get me into trouble, I think everything will work properly with a limsup (Besicovitch uses these upper means in his own investigation of the almost periodics). Then we look at locally $p$-integrable functions finite under this seminorm (a real seminorm this time), which will be a Banach space after modding out and completing (if necessary). | |
| Mar 2, 2014 at 19:19 | comment | added | Gerald Edgar | And if the limit exists for $f$ and $g$, does it follow that it also exists for $f+g$? Greg, you say it is a Banach space, but perhaps you should explain. | |
| Mar 2, 2014 at 19:06 | comment | added | Yemon Choi | Simple-minded question: why does the limit in your defining formula exist? or do you have to build that into your definition of $M^p$? | |
| Mar 2, 2014 at 15:14 | comment | added | Greg Zitelli | Of course. The $B^p$ functions have all the nice properties, like plenty of $epsilon$-translation numbers, which make them almost periodic. The $M^p$ functions almost just seem like a nice place to house the $B^p$. | |
| Mar 2, 2014 at 13:13 | comment | added | Gerald Edgar | I would not call $M^p$ functions (such as your $f$) "almost periodic" at all. | |
| Mar 2, 2014 at 3:20 | history | asked | Greg Zitelli | CC BY-SA 3.0 |