Fredholm alternative: compact K implies finite-dim eigenspace or unique solve

Fredholm 1903 (Acta Math. 27:365) for a compact integral operator (Kφ)(x) = ∫_a^b K(x,y)·φ(y) dy with square-integrable kernel: the equation φ − λKφ = g admits the following alternative. Either (i) the homogeneous equation φ = λKφ has…