A \(C^*\)-algebra generated by almost-periodic two-dimensional singular operators with discontinuous symbols (Q1110078)

An algebra \({\mathcal R}\) of almost periodic singular integral operators on \(CAP({\mathbb{R}}^ 2)\) is investigated modulo \({\mathcal K}\) (the ideal of generalized compact operators in \({\mathcal R})\); this algebra is generated by an algebra of almost periodic pseudo-differential operators and by operators \(P_ k(D)\) where \(P_ k(\xi)\) are characteristic functions of sectors in \({\mathbb{R}}^ 2\). A criterium of the generalized Noetherenianness for operators in \({\mathcal R}\) is obtained and the generalized index of the operator \(A=\sum^{m}_{1}a_ k(x)b_ k(D)P_ k(D)\) is calculated.