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

• Published in: Proceedings of the Steklov Institute of Mathematics Vol. 308; no. 1; pp. 155 - 167
• Main Authors: Denisenko, V. V., Deundyak, V. M.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Moscow Pleiades Publishing 2020; Springer Nature B.V
• Subjects: Calculus; Integrals; Kernels; Mathematical analysis; Mathematics; Mathematics and Statistics; Operators (mathematics)
• ISSN: 0081-5438; 1531-8605
• DOI: 10.1134/S0081543820010125

We consider the Heisenberg group ℍ
n
with Korányi norm. In the space
L
2
(ℍ
n
), we introduce integral operators with homogeneous kernels of compact type and multiplicatively weakly oscillating coefficients. For the unital
C
*-algebra
W
(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
W
(ℍ
n
) to be a Fredholm operator.