let be the function w(x) that only takes discrete values in the sense that is only defined for x=n being n an integer..then my question is if the integral:

[tex]\int_{-\infty}^{\infty}dxw(x)f(x)[/tex]

would be equal to the sum of the serie:

[tex]\sum_{n=-\infty}^{\infty}w(n)f(n) [/tex]

if the sum and integral would be equal imply that the function

[tex]w(x)=g(x)\sum_{-\infty}^{\infty}\delta(x-n) [/tex]

thanks...

[tex]\int_{-\infty}^{\infty}dxw(x)f(x)[/tex]

would be equal to the sum of the serie:

[tex]\sum_{n=-\infty}^{\infty}w(n)f(n) [/tex]

if the sum and integral would be equal imply that the function

[tex]w(x)=g(x)\sum_{-\infty}^{\infty}\delta(x-n) [/tex]

thanks...

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