On the algebra of singular integral operators with an inverse shift in the space \(L_p(\mathbb{R},\rho)\). (Russian. English summary) Zbl 0892.47054
Summary: In the space \(L_p(\mathbb{R},\rho)\), we study the algebras generated by singular operators with a shift and piecewise continuous coefficients. It is proved that this algebra is equivalent to a Banach algebra of singular operators without shift. This allows to define the symbol and to formulate in terms of the symbol criteria of the Fredholmness and to deduce a formula of computing the index.
MSC:
47G10 | Integral operators |
47B38 | Linear operators on function spaces (general) |
45E05 | Integral equations with kernels of Cauchy type |
47A53 | (Semi-) Fredholm operators; index theories |
47L10 | Algebras of operators on Banach spaces and other topological linear spaces |