Geodesic
Conditions for unique solvability of the matrix equation $AX+X^\ast B=C$
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 5, pp. 775-783

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Conditions for the unique solvability of the matrix equation $AX+X^\ast B=C$ are formulated in terms of the eigenvalues and the Kronecker structure of the matrix pencil $A+\lambda B^\ast$ associated with this equation. 
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     title = {Conditions for unique solvability of the matrix equation $AX+X^\ast B=C$},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     number = {5},
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Yu. O. Vorontsov; Kh. D. Ikramov. Conditions for unique solvability of the matrix equation $AX+X^\ast B=C$. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 52 (2012) no. 5, pp. 775-783. http://geodesic.mathdoc.fr/item/ZVMMF_2012_52_5_a1/