@article{f6ebfb57cb2c4cff91db96f6d0cde1d5,
title = "On algebras of two dimensional singular integral operators with homogeneous discontinuities in symbols",
abstract = "We describe the Fredholm symbol algebra for the C*-algebra generated by two dimensional singular integral operators, acting on L2(ℝ2), and whose symbols admit homogeneous discontinuities. Locally these discontinuities are modeled by homogeneous functions having slowly oscillating (and, in particular, piecewise continuous) discontinuities on a system of rays outgoing from the origin. These results extend the well-known Plamenevsky results for the two dimensional case. We present here an alternative and much clearer approach to the problem.",
author = "Karapetyants, {A. N.} and Rabinovich, {V. S.} and Vasilevski, {N. L.}",
note = "Funding Information: The principal contribution in this direction has been made by B. A. Plamenevsky (see, for example \[9\]a, nd the references there). He developed the (multidimensional) theory for the case when the points of discontinuities are modeled by homogeneous of zero order functions with continuous restrictions onto the unit sphere. Applying the Mellin transform *Postdoctoral Lefschets fellowship, CINVESTAV,M ~xico, on leave from Rostov State University, Russia. tPartially supported by Russian Fund for Fundamental Investigations, RFFI-98-01-01-023, and by CONACYT project 32424-E /Partially supported by CONACYT Project 27934-E, M6xico.",
year = "2001",
month = jul,
doi = "10.1007/BF01299848",
language = "Ingl{\'e}s",
volume = "40",
pages = "278--308",
journal = "Integral Equations and Operator Theory",
issn = "0378-620X",
number = "3",
}