Timeline for A corollary to Stone-Weierstrass theorem
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 19, 2012 at 15:02 | comment | added | zapkm | ohh sorry.. i got.. and thanks for the time... | |
| Mar 19, 2012 at 14:38 | comment | added | Mohan Ramachandran | contd:the polynomials referred to are holomorphic. | |
| Mar 19, 2012 at 14:36 | comment | added | Mohan Ramachandran | You are confusing approximation and extension. You can certainly approximate f on K uniformly by polynomials .In your example this is easy to do directly . | |
| Mar 19, 2012 at 11:52 | comment | added | zapkm | May be i am making mistake.. Please have the following example: Take K any smooth curve which doesn't passes through $(0,0)∈\mathbb C$. Take $f(z)=\frac{1}{z}$, on K, f is continuous, and $\mathbb C−K$ is connected. But f can't be extended to a entire function.... So the theorem you mention seems to have some problem. | |
| Feb 8, 2012 at 21:19 | comment | added | Mohan Ramachandran | Yes but the poles of the rational function are outside a neighbourhood of gamma . | |
| Feb 8, 2012 at 19:50 | vote | accept | zapkm | ||
| Feb 8, 2012 at 19:50 | comment | added | zapkm | Thanks for the answer: But i didn't see this extended version of Hartogs-Rosenthal theorem: I thought that theorem guarantees for the approximation by RATIONAL function. It will be very helpful for me if you can provide some reference. Thanks a lot. | |
| Feb 8, 2012 at 19:02 | history | answered | Mohan Ramachandran | CC BY-SA 3.0 |