smooth function as a sum of rect or tri functions
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At the beginning it looks to me easy but i am cannot find a mathematical prove for this. I am trying to prove that smooth function cannot be written as a sum of rect functions (or tri functions) for example let say that f(x) is a smooth function i want to prove that it cannot be written as: $ fleft(xright):=:sum _{n=0}^{infty }left(a_n:rectleft(ncdot :gleft(xright)right)right)$ and the same for the tri function: $ fleft(xright):=:sum _{n=0}^{infty }left(a_n:trileft(ncdot :gleft(xright)right)right)$ Thanks edit: The definition of the rect and tri functions: Rectangular function:: $operatorname{rect}(t) = Pi(t) = begin{cases} 0 & text{if } |t| > frac{1}{2}, \ frac{1}{2} & text{if } |t| = frac{1}{2}, \ 1 & text{if } |t| < frac{1}{2}. end{cases}$ Triangular_fu
