We find the criteria for the solvability of the operator equation , where , and are unbounded operators, and use the result to show existence and regularity of solutions of nonhomogeneous Cauchy problems.
"On the operator equation $AX - XB = C$ with unbounded operators $A,B$, and $C$." Abstr. Appl. Anal. 6 (6) 317 - 328, 10 December 2001. https://doi.org/10.1155/S1085337501000665