Let \(k\ge0\) be an integer and define \[ f_n(x)=\frac{x^k}{x^2+n},\qquad x\in\mathbb R,\quad n=1,2,\ldots. \] For which values of \(k\) does \((f_n)\) converge uniformly on \(\mathbb R\)? For which values does it converge uniformly on every bounded subset of \(\mathbb R\)?
Uniform convergence of $x^k/(x^2+n)$ on bounded and unbounded sets
P-BKS78-1
- Area
- Prelim
- Seen at
- BERKELEY
- Years
- 1978
- Status
- draft