Main Results
The classical results of the theory are Fredholm's theorems, one of which is the Fredholm alternative.
One of the important results from the general theory are that the kernel is a compact operator when the space of functions are equicontinuous.
A related celebrated result is the Atiyah–Singer index theorem, pertaining to index (dim ker – dim coker) of elliptic operators on compact manifolds.
Read more about this topic: Fredholm Theory
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