Some properties of the resolvent kernels for integral equations with
Dalʹnevostočnyj matematičeskij žurnal, Tome 16 (2016) no. 2, pp. 186-208.

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We prove that, at regular values lying in a region of generalized strong convergence, the resolvent kernels corresponding to a continuous bi-Carleman kernel vanishing at infinity can be expressed as uniform limits of sequences of resolvent kernels associated with its approximating Hilbert-Schmidt-type subkernels.
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I. M. Novitskii. Some properties of the resolvent kernels for integral equations with. Dalʹnevostočnyj matematičeskij žurnal, Tome 16 (2016) no. 2, pp. 186-208. http://geodesic.mathdoc.fr/item/DVMG_2016_16_2_a7/

[1] Siberian Math. J., 39 (1998), 781–783 | DOI | MR | Zbl

[2] V. B. Korotkov, Introduction to the algebraic theory of integral operators, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok, 2000, 79 pp. (in Russian)

[3] Siberian Adv. Math., 7 (1997), 5–17 | MR | MR | Zbl

[4] T. Carleman, Sur les équations intégrales singulières à noyau réel et symétrique, A.-B. Lundequistska Bokhandeln, Uppsala, 1923

[5] J. von Neumann, Charakterisierung des Spektrums eines Integraloperators, Actual. scient. et industr., 229, Hermann, Paris, 1935 (in German)

[6] W. J. Trjitzinsky, “Singular integral equations with complex valued kernels”, Ann. Mat. Pura Appl., 4:25 (1946), 197–254 | DOI | MR

[7] N. I. Akhiezer, “Integral operators with Carleman kernels”, Uspekhi Mat. Nauk., 2:5 (1947), 93–132 (in Russian) | MR | Zbl

[8] Monographs and Studies in Mathematics, 9, 10, Pitman Advanced Publishing Program, Boston, 1981 | MR | Zbl

[9] C. G. Costley, “On singular normal linear equations”, Can. Math. Bull., 13 (1970), 199–203 | DOI | MR | Zbl

[10] J. W. Williams, “Linear integral equations with singular normal kernels of class I”, J. Math. Anal. Appl., 68:2 (1979), 567–579 | DOI | MR | Zbl

[11] V. B. Korotkov, Integral operators, Nauka, Novosibirsk, 1983 (in Russian) | Zbl

[12] T. Kato, Perturbation theory for linear operators, Corr. print. of the 2nd ed., Springer-Verlag, Berlin-Heidelberg-New York, 1980 | MR | Zbl

[13] E. Hille, Functional analysis and semi-groups, Amer. Math. Soc. Colloq. Publ. 31, New York, 1948 | MR | Zbl

[14] Pergamon Press, Oxford-Elmsford-New York, 1982 | MR | Zbl | Zbl

[15] P. Halmos, V. Sunder, Bounded integral operators on $L^2$ spaces, Springer, Berlin, 1978 | MR

[16] M. Reed, B. Simon, Methods of modern mathematical physics. {I}. Functional analysis, rev. ed., Academic Press, San Diego, 1980 | MR | Zbl

[17] B. Misra, D. Speiser, G. Targonski, “Integral operators in the theory of scattering”, Helv. Phys. Acta, 36 (1963), 963–980 | MR | Zbl

[18] A. C. Zaanen, “An extension of Mercer's theorem on continuous kernels of positive type”, Simon Stevin, 29 (1952), 113–124 | MR | Zbl

[19] J. Buescu, “Positive integral operators in unbounded domains”, J. Math. Anal. Appl., 296:1 (2004), 244–255 | DOI | MR | Zbl

[20] Differential Equations, 28:9 (1992), 1329–1337 | MR

[21] Soviet Math. Dokl., 43:3 (1991), 874–877 | MR

[22] I. M. Novitskii, “Integral representations of linear operators by smooth Carleman kernels of Mercer type”, Proc. Lond. Math. Soc. (3), 68:1 (1994), 161–177 | DOI | MR

[23] T. Carleman, “Zur Theorie der linearen Integralgleichungen”, Math. Z., 9 (1921), 196–217 | DOI | MR | Zbl

[24] S. G. Mikhlin, “On the convergence of Fredholm series”, Doklady AN SSSR, XLII:9 (1944), 374–377 (in Russian) | MR

[25] F. Smithies, “The Fredholm theory of integral equations”, Duke Math. J., 8 (1941), 107–130 | DOI | MR