# Uniqueness of the Solution to Fredholm's Integral Equations of the First Kind

Any one who knows the conditions for Uniqueness of the Solution to Fredholm's Integral Equations of the First Kind?

Thanks.

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Since Fredholm integral operators tend to be compact (for example if considered as operators $L^2 \to L^2$), I think uniqueness would be rather rare – user38355 Dec 5 '12 at 23:37