Atomic function

Atomic function \mathrm{up}(x) and it’s properties

    \begin{eqnarray*} &y'(x)=2y(2x+1)-2y(2x-1), \\ &\mathrm{supp}(\mathrm{up}(x))=\left[-1,1\right], \\ &\displaystyle\int\limits_{-1}^1\mathrm{up}(x)dx=1, \\ &\widehat{\mathrm{up}}(t)=\prod\limits_{k=1}^{\infty}{\mathrm{sinc}\biggl(\dfrac{t}{2^{k}}\biggr)}, \\ &\mathrm{up}(x)=\dfrac{1}{2}+\sum\limits_{k=1}^{\infty}\widehat{\mathrm{up}}(\pi k)\cos(\pi k x). \end{eqnarray*}

Written by

Skip to toolbar