The Fredholm Alternative of Theorem 5.55 first appeared in the study of what are now known as
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in which K(x, y) and f(x) are prescribed continuous functions. Explain how the integral equation is a linear system; i.e., describe the linear map L, its domain and target spaces, and prove linearity.
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n(x) +1 K(x, y) u(v) dv=f(x).
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