ON THE ALGEBRA GENERATED BY CANONICAL INTEGRAL OPERATORS WITH HOMOGENEOUS KERNELS

We consider the Banach algebra \(\mathfrak {A}\) $\mathfrak{A}$ generated by multidimensional integral operators whose kernels are homogeneous of degree \((-n)\) $(-n)$ and invariant with respect to all rotations of the space \(\mathbb {R}^n\) ${\mathbb{R}}^n$ . We construct a symbolic calculus for this algebra. In terms of this calculus, we obtain the necessary and sufficient conditions for an operator in \(\mathfrak {A}\) $\mathfrak{A}$ to be invertible and Fredholm.