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The Smoluchowski diffusion equation, represented as the eigenvalue equation for the adjoint of the diffusion operator, has been solved by computing averages obtained along with the MD statistics.
Suffice it to say that adjoint functors pervade mathematics and this pervasiveness is certainly one of the most mysterious fact that category theory reveals about mathematics and probably thinking in general.
He then went on to consider the case where the kernel is not symmetric and showed that in that case the eigenfunctions associated with a given eigenvalue occurred in adjoint pairs.
For the case of a finite-dimensional real linear space these are infinite systems whose adjoint cone is topologically closed.
He reproved the earlier results and gave new results of his own on minors and adjoints .
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