Spectral analysis for a class of integral-difference operators: known facts, new results, and open problems
The author presents a review of the existing literature on the spectral analysis of integral-difference operators of the form \[ {\mathcal K}_\phi:u(x)\mapsto \int_\infty^\infty \frac{u(x)\phi (s)-u(s)\phi (x)}{| x-s| }ds \] acting on \(L_2({\mathbb R},dx)\), where \(\phi(x)\) is a probability function on \(\mathbb R\). These operators appear in some non-equilibriun statistical physics models as collision operators.
scientific article; zbMATH DE number 2148592