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On algebras of two dimensional singular integral operators with homogeneous discontinuities in symbols

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Abstract

We describe the Fredholm symbol algebra for theC *-algebra generated by two dimensional singular integral operators, acting onL 2(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.

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Authors and Affiliations

  1. Departamento de Matemáticas, CINVESTAV del I.P.N., Apartado Postal 14-740, 07000, México, D.F., México

    A. N. Karapetyants (Postdoctoral Lefschets fellowship) & N. L. Vasilevski

  2. Departamento de Telecomunicaciones, ESIME del I.P.N., Unidad Zacatenco, Av. I.P.N. s/n, Ed. 1, 07738, México, D.F., México

    V. S. Rabinovich

Authors
  1. A. N. Karapetyants
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  2. V. S. Rabinovich
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  3. N. L. Vasilevski
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Rostov State University Russia

Partially 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, México.

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Karapetyants, A.N., Rabinovich, V.S. & Vasilevski, N.L. On algebras of two dimensional singular integral operators with homogeneous discontinuities in symbols. Integr equ oper theory 40, 278–308 (2001). https://doi.org/10.1007/BF01299848

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