FA24

From Exampleproblems

Let $L^2[a,b]=\left\{f:\int_a^b\left|f(t)\right|^2 dt < \infty\right\}\,$ and define $||f||=\left(\int_a^b\left|f(t)\right|^2 dt\right)^{1/2}\,$ . Show that

$(Tf)(t) = \int_a^b K(s,t)f(s)ds\,$

defines a bounded linear operator on $L^2[a,b]\,$ when $K(s,t)\,$ is a continuous function on $[a,b]\times[a,b]\,$ . Estimate the norm of $T\,$ .

FA24

From Exampleproblems

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