This article is cited in 6 papers

Fredholm Property of Integral Operators with Homogeneous Kernels of Compact Type in the $L_2$ Space on the Heisenberg Group

V. V. Denisenko, V. M. Deundyak

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

Abstract: We consider the Heisenberg group $\mathbb H_n$ with Korányi norm. In the space $L_2(\mathbb H_n)$, we introduce integral operators with homogeneous kernels of compact type and multiplicatively weakly oscillating coefficients. For the unital $C^*$-algebra $\mathfrak W(\mathbb H_n)$ generated by such operators, we construct a symbolic calculus and in terms of this calculus formulate necessary and sufficient conditions for an operator in $\mathfrak W(\mathbb H_n)$ to be a Fredholm operator.

UDC: 517.983

Received: April 1, 2019
Revised: October 9, 2019
Accepted: December 3, 2019

DOI: 10.4213/tm4058

 English version: Proceedings of the Steklov Institute of Mathematics, 2020, 308, 155–167

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