While doing physics research, I`ve come across the linear operator $$(K\phi)(t_{2}):=\text{P.V}\int_{-1}^{1}\frac{\phi(t_{1})}{(t_{1}-t_{2})}dt_{1}$$ with arguments and values in functions on $[-1,1]$. The functional of my interest is extremized by eigenfunctions of $K$ - do such functions exist? Is there some good literature on this operator? - preferably, accessible by a physicist.
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