@inbook{616eea4f5bdd426e8580c718b781ff65,

title = "A C∗-algebra of Singular Integral Operators with Shifts and Piecewise Quasicontinuous Coefficients",

abstract = "The C∗-algebra B of bounded linear operators on the space L2}T, which is generated by all multiplication operators by piecewise quasicontinuous functions, by the Cauchy singular integral operator and by the range of a unitary representation of a group G of orientation-preserving diffeomorphisms of T onto itself that have the same finite set of fixed points for all (Formula presented), is studied. A Fredholm symbol calculus for the C∗-algebra B and a Fredholm criterion for the operators (Formula presented) are established by using spectral measures and the local-trajectory method for studying C∗-algebras associated with C∗-dynamical systems.",

keywords = "Amenable group, C-algebra, Fredholmness, Local-trajectory method, Piecewise quasicontinuous function, Representation of a C-algebra, Singular integral operator with shifts, Spectral measure, Symbol calculus",

author = "Bastos, {M. Am{\'e}lia} and Fernandes, {Cl{\'a}udio A.} and Karlovich, {Yuri I.}",

year = "2018",

month = jan,

day = "1",

doi = "10.1007/978-3-319-72449-2_2",

language = "English",

series = "Operator Theory: Advances and Applications",

publisher = "Springer International Publishing Switzerland",

pages = "25--64",

booktitle = "Operator Theory: Advances and Applications",

}