### CAS Seminar

# Haidar Mohamad

### (Jacobs University)

## "The operator equation \(\sum_{i=1}^n A^{n-i}XB^{i-1} = Y\) and a specific application"

** Date: ** |
Wed, September 27, 2017 |

** Time: ** |
14:15 |

** Place: ** |
Research I Seminar Room |

**Abstract:** The solution of the linear operator equation \(\sum_{i=1}^n A^{n-i} XB^{i-1} = Y\) is given by the integral formula \(X= \frac{\sin(\pi /n)}{\pi} \int_0^\infty t^{1/ n} (t+A^n)^{-1}Y(t+B^n)^{-1}dt \) if \(A, B\) are bounded normal, \(Y\) is bounded on a complex Hilbert space with spectrum in \(\{z\neq 0, -\pi/(2n) < Arg(z) < \pi/(2n)\}\).