Asymptotische Approximation stetiger Funktionen durch Funktionenreihen. (Asymptotic approximation of continuous functions by series of functions) (Q1107048)

The asymptotic approximation of given continuous functions by functional series is of great importance. Here the author deals with this question in certain special contexts using various specific series. Eight theorems are stated proved and discussed. An important example of the theorems is: For every polynomial \(P(x)=\sum^{N}_{k=1}b_ kx\quad k,\) \(b_ N\neq 0\), \(N\geq 1\) there exists a \(d>0\), such that the covering functional system S with \(K_ n(s)=P(de^{sn})\) \((-\infty <s<\infty)\) has the desired asymptotic property \((A_{\infty})\).