An essay on some problems of approximation theory
| dc.creator | Ramm, A. G. | |
| dc.date | 2003-01-31 | |
| dc.date.accessioned | 2026-07-07T04:54:49Z | |
| dc.date.available | 2026-07-07T04:54:49Z | |
| dc.description | Several questions of approximation theory are discussed: 1) can one approximate stably in $L^\infty$ norm $f^\prime$ given approximation $f_δ, \parallel f_δ- f \parallel_{L^\infty} < δ$, of an unknown smooth function $f(x)$, such that $\parallel f^\prime (x) \parallel_{L^\infty} \leq m_1$? 2) can one approximate an arbitrary $f \in L^2(D), D \subset \R^n, n \geq 3$, is a bounded domain, by linear combinations of the products $u_1 u_2$, where $u_m \in N(L_m), m=1,2,$ $L_m$ is a formal linear partial differential operator and $N(L_m)$ is the null-space of $L_m$ in $D$, $3) can one approximate an arbitrary $L^2(D)$ function by an entire function of exponential type whose Fourier transform has support in an arbitrary small open set? Is there an analytic formula for such an approximation? N(L_m) := \{w: L_m w=0 \hbox{in\} D\}$? | |
| dc.identifier | https://arxiv.org/abs/math/0301380 | |
| dc.identifier | http://arxiv.org/abs/math/0301380 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66407 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 41-XX, 30D20, 35R25, 35J10, 35J05, 65M30 | |
| dc.title | An essay on some problems of approximation theory | |
| dc.type | text |