On the \(C^*\)-algebra generated by multidimensional integral operators with homogeneous kernels and multiplicative translations (Q951726)

The paper investigates the \(C^{\ast}\)-algebra generated by integral operators on \(L_{2}({\mathbb R}^{n})\) with kernel homogeneous of degree \((-n)\) and invariant under the rotation group in \({\mathbb R}^{n}\), and by multiplicative translation operators (operators on the form \(f(x)\rightarrow \delta^{-n/2}f(x/\delta)\), \(\delta>0\)). The author gives a description of the structure of this algebra and constructs a symbolic calculus, in terms of which a criterion of invertibility and Fredholmness is formulated.