Mathematics – Classical Analysis and ODEs
Scientific paper
2003-01-31
Mathematics
Classical Analysis and ODEs
Scientific paper
Several questions of approximation theory are discussed: 1) can one approximate stably in $L^\infty$ norm $f^\prime$ given approximation $f_\delta, \parallel f_\delta - f \parallel_{L^\infty} < \delta$, 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\}$?
No associations
LandOfFree
An essay on some problems of approximation theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with An essay on some problems of approximation theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An essay on some problems of approximation theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-390792