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Characterization of an integral operator with a Bessel kernel
I am considering the following integral operator: $$K(\sigma)(\theta)=\int_0^{2\pi} \sigma(\theta') J_0(|e^{i\theta}-e^{i\theta'}|)\,d\theta',$$ where $J_0$ is the Bessel function of order $0.$
I am ...
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Are there any functions $f$ beyond trivial examples where $\int f(x +f(x + f(x +\dotsb)))\,dx$ $= F(x+F(x+F(x +\dotsb))) + C$ for some function $F$?
Basically the title explains most of my question here. Purely out of curiosity (I have no real application), I am wondering if there are any "interesting" functions $f$ where we know of a ...
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