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Fredholm Property of Integral Operators with Homogeneous Kernels of Compact Type in the L2 Space on the Heisenberg Group

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Abstract

We consider the Heisenberg group ℍn with Korányi norm. In the space L2(ℍn), we introduce integral operators with homogeneous kernels of compact type and multiplicatively weakly oscillating coefficients. For the unital C*-algebra \(\mathfrak{W}\)(ℍn) generated by such operators, we construct a symbolic calculus and in terms of this calculus formulate necessary and sufficient conditions for an operator in \(\mathfrak{W}\)(ℍn) to be a Fredholm operator.

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Authors and Affiliations

  1. Institute of Mathematics, Mechanics, and Computer Science named after I. I. Vorovich, Southern Federal University, ul. Mil’chakova 8a, Rostov-on-Don, 344090, Russia

    V. V. Denisenko & V. M. Deundyak

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  1. V. V. Denisenko
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  2. V. M. Deundyak
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Correspondence to V. V. Denisenko or V. M. Deundyak.

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Russian Text © The Author(s), 2020, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Vol. 308, pp. 167–180.

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Denisenko, V.V., Deundyak, V.M. Fredholm Property of Integral Operators with Homogeneous Kernels of Compact Type in the L2 Space on the Heisenberg Group. Proc. Steklov Inst. Math. 308, 155–167 (2020). https://doi.org/10.1134/S0081543820010125

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