(Solution) - Integral Transforms If K s t is a continuous function of -(2025 Original AI-Free Solution)

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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.