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 Tr. Mat. Inst. Steklova, 2020, Volume 308, Pages 167–180 (Mi tm4058)

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.

DOI: https://doi.org/10.4213/tm4058

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

Bibliographic databases:

UDC: 517.983
Revised: October 9, 2019
Accepted: December 3, 2019

Citation: V. V. Denisenko, V. M. Deundyak, “Fredholm Property of Integral Operators with Homogeneous Kernels of Compact Type in the $L_2$ Space on the Heisenberg Group”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 308, Steklov Math. Inst. RAS, Moscow, 2020, 167–180; Proc. Steklov Inst. Math., 308 (2020), 155–167

Citation in format AMSBIB
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