Geodesic
Integral operators with the~generalized sine kernel on the~real axis
Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 1, pp. 32-47

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We study the asymptotic properties of integral operators with the generalized sine kernel acting on the real axis. We obtain the formulas for the Fredholm determinant and the resolvent in the large-$x$ limit and consider some applications of the obtained results to the theory of integrable models.
Keywords: Fredholm determinant, resolvent, asymptotic expansion. 
@article{TMF_2010_165_1_a2,
     author = {N. A. Slavnov},
     title = {Integral operators with the~generalized sine kernel on the~real axis},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {32--47},
     publisher = {mathdoc},
     volume = {165},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_165_1_a2/}
}
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N. A. Slavnov. Integral operators with the~generalized sine kernel on the~real axis. Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 1, pp. 32-47. http://geodesic.mathdoc.fr/item/TMF_2010_165_1_a2/