Geodesic
Integral operators with the generalized sine kernel on the real axis
Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 1, pp. 32-47 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

[1] M. Gaudin, Nucl. Phys., 25 (1961), 447–458 | DOI | Zbl

[2] M. L. Mehta, M. Gaudin, Nucl. Phys., 18 (1960), 420–427 | DOI | MR | Zbl

[3] A. Lenard, J. Math. Phys., 5:7 (1964), 930–943 | DOI | MR

[4] M. Jimbo, T. Miwa, Y. Môri, M. Sato, Physica D, 1:1 (1980), 80–158 | DOI | MR | Zbl

[5] J. des Cloizeaux, M. L. Mehta, J. Math. Phys., 14:11 (1973), 1648–1650 | DOI | MR | Zbl

[6] H. Widom, Indiana Univ. Math. J., 21 (1971), 277–283 | DOI | MR | Zbl

[7] F. Dyson, Comm. Math. Phys., 47:2 (1976), 171–183 | DOI | MR | Zbl

[8] H. Widom, J. Approx. Theory, 77:1 (1994), 51–64 | DOI | MR | Zbl

[9] H. Widom, Comm. Math. Phys., 171:1 (1995), 159–180, arXiv: hep-th/9405010 | DOI | MR | Zbl

[10] V. I. Krasovsky, Int. Math. Res. Not., 25 (2004), 1249–1272 | DOI | MR | Zbl

[11] T. Ehrhardt, Comm. Math. Phys., 262:2 (2006), 317–341 | DOI | MR | Zbl

[12] P. A. Deift, A. R. Its, I. Krasovsky, X. Zhou, J. Comput. Appl. Math., 202:1 (2007), 26–47, arXiv: math/0601535 | DOI | MR | Zbl

[13] A. M. Budylin, V. S. Buslaev, Algebra i analiz, 7:6 (1995), 79–103 | MR | Zbl

[14] P. A. Deift, A. R. Its, X. Zhou, Ann. Math., 146:1 (1997), 149–235 | DOI | MR | Zbl

[15] V. A. Fok, Matem. sb., 14:1–2 (1944), 3–50 | MR | Zbl

[16] B. Nobl, Primenenie metoda Vinera–Khopfa dlya resheniya differentsialnykh uravnenii v chastnykh proizvodnykh, IL, M., 1962 | MR | MR | Zbl

[17] B. M. McCoy, J. H. H. Perk, R. E. Shrock, Nucl. Phys. B, 220:1 (1983), 35–47 | DOI | MR

[18] A. Lenard, J. Math. Phys., 7:7 (1966), 1268–1272 | DOI | MR

[19] A. R. Its, A. G. Izergin, V. E. Korepin, Comm. Math. Phys., 129:1 (1990), 205–222 | DOI | MR | Zbl

[20] A. R. Its, A. G. Izergin, V. E. Korepin, Comm. Math. Phys., 130:3 (1990), 471–488 | DOI | MR | Zbl

[21] F. Colomo, A. G. Izergin, V. E. Korepin, V. Tognetti, Phys. Lett. A, 169:4 (1992), 243–247 | DOI | MR

[22] F. Colomo, A. G. Izergin, V. E. Korepin, V. Tognetti, TMF, 94:1 (1993), 19–51 | DOI | MR

[23] A. R. Its, A. G. Izergin, V. E. Korepin, N. A. Slavnov, Phys. Rev. Lett., 70:11 (1993), 1704–1706 ; Erratum: 70:15, 2357–2357, arXiv: hep-th/9212135 | DOI | DOI

[24] A. R. Its, A. G. Izergin, V. E. Korepin, N. A. Slavonv, Internat J. Modern Phys. B, 4:5 (1990), 1003–1037 | DOI | MR | Zbl

[25] V. V. Cheianov, M. R. Zvonarev, J. Phys. A, 37:6 (2004), 2261–2297, arXiv: cond-mat/0310499 | DOI | MR | Zbl

[26] N. Kitanine, K. K. Kozlowski, J.-M. Maillet, N. A. Slavnov, V. Terras, Comm. Math. Phys., 291:3 (2009), 691–761, arXiv: 0805.4586 | DOI | MR | Zbl

[27] P. Deift, “Integrable operators”, Differential Operators and Spectral Theory, M. Sh. Birman's 70th anniversary collection, Amer. Math. Soc. Transl. Ser. 2, 189, eds. V. Buslaev, M. Solomyak, D. Yafaev, AMS, Providence, R.I., 1999, 69–84 | MR | Zbl

[28] N. I. Akhiezer, Ukr. matem. zhurn., 16 (1964), 445–462 | MR | Zbl

[29] A. G. Izergin, V. E. Korepin, Comm. Math. Phys., 94:1 (1984), 67–92 | DOI | MR | Zbl

[30] A. G. Izergin, V. E. Korepin, Comm. Math. Phys., 99:2 (1985), 271–302 | DOI | MR | Zbl

[31] V. E. Korepin, N. M. Bogoliubov, A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge Monogr. Math. Phys., Cambridge Univ. Press, Cambridge, 1993 | MR | Zbl

[32] V. E. Korepin, Comm. Math. Phys., 86:3 (1982), 391–418 | DOI | MR | Zbl