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 – Dec 05 '12 at 23:37
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@user38355, this is a gap for me. Any references you’d recommend? – A rural reader Feb 28 '23 at 23:18
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1Asanov (2019) "About Uniqueness of Solutions of Fredholm Linear Integral Equations of the First Kind in the Axis" for a general characterisation, Han (2015) "The necessary and sufficient condition for the existence and uniqueness of a system of Fredholm integral equations of the first kind" in Chinese for determining uniqueness in a specific case of Laplace's equation. – ə̷̶̸͇̘̜́̍͗̂̄︣͟ Mar 03 '23 at 02:13
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See, for example, https://www.colorado.edu/amath/sites/default/files/attached-files/fredholm.pdf – S. Catterall Mar 07 '23 at 12:14