We consider the Heisenberg group ℍ_n with Korányi norm. In the space L₂(ℍ_n), we introduce integral operators with homogeneous kernels of compact type and multiplicatively weakly oscillating coefficients. For the unital C*-algebra \(\mathfrak{W}\)(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 \(\mathfrak{W}\)(ℍ_n) to be a Fredholm operator.

中文翻译：

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Heisenberg群上L 2空间中具有紧型齐次核的积分算子的Fredholm性质。

我们认为海森堡组ℍ _ň与Korányi规范。在空间大号₂（ℍ _Ñ），介绍与紧凑型的均匀内核和乘法弱振荡系数积分算。对于酉Ç * -代数\（\ mathfrak【W} \）（ℍ _Ñ由这样的运营商产生的），我们构建了一个符号演算和在该演算方面制定的充分必要条件为在运营商\（\ mathfrak {白} \）（ℍ _ñ）是一个Fredholm算子。