Geodesic
Spectral properties of a certain class of Carleman operators
Archivum mathematicum, Tome 43 (2007) no. 3, pp. 163-175.

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The object of the present work is to construct all the generalized spectral functions of a certain class of Carleman operators in the Hilbert space $L^{2}\left( X,\mu \right) $ and establish the corresponding expansion theorems, when the deficiency indices are (1,1). This is done by constructing the generalized resolvents of $A$ and then using the Stieltjes inversion formula.
Classification : 05C38, 15A15
Keywords: spectral theory; integral operator; defect indices 
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Bahri, S. M. Spectral properties of a certain class of Carleman operators. Archivum mathematicum, Tome 43 (2007) no. 3, pp. 163-175. http://geodesic.mathdoc.fr/item/ARM_2007__43_3_a2/