On the denseness of the compactly supported functions in weighted spaces (Q1062248)

From author's introduction: ''For a function in a weighted seminormed space \(L^{r_ n}_{p,\phi}(J_ n)\) we construct a sequence of compactly supported infinitely differentiable functions that converges in the seminorm to the given function, and we determine the rate of convergence of this sequence''. The author notes further that analogous results were proved by \textit{E. T. Poulsen} [Math. Scand. 10, 45-52 (1962; Zbl 0104.332)] with the help of some different methods. The methods of the paper under review are more effective.