Algebras of convolution type operators with non-regular data.

Autor: Yuri Karlovich
The Banach algebra of convolution type operators with piecewise slowly oscillating data is studied on weighted Lebesgue spaces with Muckenhoupt weights. A Fredholm symbol calculus for this algebra is constructed and a Fredholm criterion for the operators in this algebra is established. A new approach to determine local spectra is presented. Applications to nonlocal convolution type operators are also considered.