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C*-algebra of integral operators with homogeneous kernels and oscillating coefficients

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Abstract

We consider the C*-algebra generated by multidimensional integral operators with (−n)th-order homogeneous kernels and by the operators of multiplication by oscillating coefficients of the form |x|iα. For this algebra, we construct an operator symbolic calculus and obtain necessary and sufficient conditions for the Fredholm property of an operator in terms of this calculus.

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Authors and Affiliations

  1. Southern Federal University, Rostov-on-Don, Russia

    O. G. Avsyankin

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  1. O. G. Avsyankin
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Correspondence to O. G. Avsyankin.

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Original Russian Text © O. G. Avsyankin, 2016, published in Matematicheskie Zametki, 2016, Vol. 99, No. 3, pp. 323–332.

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Avsyankin, O.G. C*-algebra of integral operators with homogeneous kernels and oscillating coefficients. Math Notes 99, 345–353 (2016). https://doi.org/10.1134/S0001434616030019

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  • DOI: https://doi.org/10.1134/S0001434616030019

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