Publications and Preprints

The operator equation $\sum_{i=0}^{n} A^{n-i} X B^i =Y$
by
Rajendra Bhatia and Mitsuru Uchiyama
The solution of the linear operator equation:\\ $A^{n-1}X+A^{n-2}XB+\cdots +AXB^{n-2}+XB^{n-1}=Y$ is given by $X= \frac{\sin \pi/n}{\pi}\int^\infty_0 (t+ A^n)^{-1} Y (t+ B^n)^{-1} t^{1/n}dt$ if the specta of $A$ and $B$ are in the sector $\{z: z\ne0, -\pi/n < \arg z < \pi /n\}$.

isid/ms/2009/02 [fulltext]