Geodesic
Fredholm formulae for kernels which are linear with respect to parameter
Dalʹnevostočnyj matematičeskij žurnal, Tome 3 (2002) no. 2, pp. 173-194

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In this paper, we construct formulae, which are similar to the classical determinant formulae of Fredholm, for solving second-kind integral equations in $L_2(\mathbb R)$ with continuous on $\mathbb R^2$ Carleman kernels of the form $H(s,t)+\mu G(s,t)$, where $\mu$ is a complex parameter 
@article{DVMG_2002_3_2_a3,
     author = {I. M. Novitskii},
     title = {Fredholm formulae for kernels which are linear with respect to parameter},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {173--194},
     publisher = {mathdoc},
     volume = {3},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2002_3_2_a3/}
}
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I. M. Novitskii. Fredholm formulae for kernels which are linear with respect to parameter. Dalʹnevostočnyj matematičeskij žurnal, Tome 3 (2002) no. 2, pp. 173-194. http://geodesic.mathdoc.fr/item/DVMG_2002_3_2_a3/