@inbook{735e4f9ba3b348a5aaac8cc15e6140a3,

title = "A C*-algebra of singular integral operators with shifts similar to affine mappings",

abstract = "Representations on Hilbert spaces for the nonlocal C*-algebra B of singular integral operators with piecewise slowly oscillating coefficients, which is extended by the unitary shift operators Ug associated with the solvable discrete group G of diffeomorphisms g : T → T that are similar to affine mappings on the real line, are constructed. Such shifts may change or preserve the orientation on T and have both common fixed points for all g Є G and distinct fixed points for different shifts. Using the theory developed for C*-algebras of singular integral operators with shifts preserving the orientation of a contour, a Fredholm symbol calculus for the C*-algebra B is constructed and a Fredholm criterion for the operators B Є B is established.",

keywords = "Affine shifts, Amenable group, C*-algebra, Fredholm-ness, Lifting theorem, Local-trajectory method, Piecewise slowly oscillating function, Representation, 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 = "2014",

language = "English",

series = "Operator Theory: Advances and Applications",

publisher = "Springer International Publishing Switzerland",

pages = "53--79",

booktitle = "Operator Theory",

}