Timeline for Approximation of analytic functions by Lp functions
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 7, 2014 at 19:45 | vote | accept | Alem | ||
| Feb 7, 2014 at 17:24 | answer | added | ahmed | timeline score: 1 | |
| Feb 6, 2014 at 9:55 | comment | added | Alem | If we expand it in Taylor series, we could cut finitely many terms and so these would be in $L^{p}\left(\mathbb{D}\right)$. So we could approximate it with some finite part of it which is obviously in $L^{\mathbb{p}}\left(\mathbb{D}\right)$. Really interesting. | |
| Feb 6, 2014 at 9:47 | comment | added | Willie Wong | Have you thought about $f = 1/(z-1)^2$? | |
| Feb 6, 2014 at 9:39 | comment | added | Alem | It is Lebesgue space. These spaces are called Bergman spaces. Let us consider the unit ball $\mathbb{D}$. If we have a function that is analytic on $\mathbb{D}$. Is there any analytic function $g\in L^{p}\left(\mathbb{D}\right)$ such that $g$ approximates $f$ on $\mathbb{D}$ in any way? Are there any results on this topic? | |
| Feb 6, 2014 at 9:32 | comment | added | Willie Wong | What exactly is $L^p$ here? The usual Lebesgue space with index $p$, or something else? If so, everything boils down to boundary behaviour, no? Then point-wise approximation feels very unlikely as it does not affect the blow-up rate. | |
| Feb 5, 2014 at 16:06 | review | Close votes | |||
| Feb 6, 2014 at 10:45 | |||||
| Feb 5, 2014 at 14:26 | comment | added | Alem | The domain is just like that that Lp of analytic functions of that domain is not zero. I didn't find anything, nor for the ball, nor for the half space etc...So any particular case would be ok for me. I would like pointwise approximation in the sense that for analytic function $f$ we have other analytic function $g\in L^{p}$ such that $\vert f-g\vert<\epsilon$. | |
| Feb 5, 2014 at 13:45 | history | asked | Alem | CC BY-SA 3.0 |