Uniform approximation of sgn(x) by rational functions with prescribed poles
| dc.creator | Peherstorfer, Franz | |
| dc.creator | Yuditskii, Peter | |
| dc.date | 2006-08-10 | |
| dc.date.accessioned | 2026-07-07T07:21:37Z | |
| dc.date.available | 2026-07-07T07:21:37Z | |
| dc.description | For $a\in (0,1)$ let $L^k_m(a)$ be the error of the best approximation of the function $\sgn(x)$ on the two symmetric intervals $[-1,-a]\cup[a,1]$ by rational functions with the only possible poles of degree $2k-1$ at the origin and of $2m-1$ at infinity. Then the following limit exists \begin{equation} \lim_{m\to \infty}L^k_m(a)(\frac{1+a}{1-a})^{m-{1/2}} (2m-1)^{k+{1/2}}=\frac 2 π(\frac{1-a^2}{2a})^{k+{1/2}} Γ(k+\frac 1 2). \end{equation} | |
| dc.identifier | https://arxiv.org/abs/math/0608253 | |
| dc.identifier | http://arxiv.org/abs/math/0608253 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115363 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | 41A44; 30E | |
| dc.title | Uniform approximation of sgn(x) by rational functions with prescribed poles | |
| dc.type | text |