C*-algebra of integral operators with homogeneous kernels and oscillating coefficients

Abstract

We consider the C*-algebra generated by multidimensional integral operators with (−n)th-order homogeneous kernels and by the operators of multiplication by oscillating coefficients of the form |x|^iα. For this algebra, we construct an operator symbolic calculus and obtain necessary and sufficient conditions for the Fredholm property of an operator in terms of this calculus.