Geodesic
Spectral sets and the Drazin inverse with applications to second order differential equations
Applications of Mathematics, Tome 47 (2002) no. 1, pp. 1-8.

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The paper defines and studies the Drazin inverse for a closed linear operator $A$ in a Banach space $X$ in the case that $0$ belongs to a spectral set of the spectrum of $A$. Results are applied to extend a result of Krein on a nonhomogeneous second order differential equation in a Banach space.
DOI : 10.1023/A:1021793115985
Classification : 34G10, 47A05, 47A10, 47A60, 47N20
Keywords: Banach space; closed linear operators; Drazin inverse; spectral sets; second order differential equations 
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Tran, Trung Dinh. Spectral sets and the Drazin inverse with applications to second order differential equations. Applications of Mathematics, Tome 47 (2002) no. 1, pp. 1-8. doi : 10.1023/A:1021793115985. http://geodesic.mathdoc.fr/articles/10.1023/A:1021793115985/

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