Integral Transforms If K(s, t) is a continuous function of s and t on the square 0 curren s curren 1, 0 curren t curren 1, and i(r)is any continuous function of t for 0 curren t curren 1 we can define the function F given by Show that the mapping T(f (t)) F(s) is a linear trans formation from C 0, 1 into itself F(s) K(s, t)f(t) dt

Question: Integral Transforms If K(s, t) is a continuous function of s and t on the square 0 ¤ s ¤ 1, 0 ¤ t ¤

Integral Transforms If K(s, t) is a continuous function of s and t on the square 0 ‰¤ s ‰¤ 1, 0 ‰¤ t ‰¤ 1, and i(r)is any continuous function of t for 0 ‰¤ t ‰¤ 1. we can define the function F given by

Show that the mapping T(f (t)) = F(s) is a linear trans-formation from C[0, 1] into itself.

F(s) = | K(s, t)f(t) dt

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