..

2016, 2, . 186-208


, , , .

:
2- , , , , , , , ,

( PDF)

[1] V.B. Korotkov, On the nonintegrability property of the Fredholm resolvent of some integral operators, Sibirsk. Mat. Zh., 39 (1998), 905907 (in Russian); English transl.: Siberian Math. J., 39 (1998), 781-783.
[2] V.B. Korotkov, Introduction to the algebraic theory of integral operators, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok, 2000, ISBN: 5-1442-0827-5 (in Russian), 79 pp.
[3] V.B. Korotkov, Some unsolved problems of the theory of integral operators, Sobolev spaces and related problems of analysis, Trudy Inst. Mat.. V. 31, Izdat. Ross. Akad. Nauk Sib. Otd. Inst. Mat., Novosibirsk, 1996, 187196 (in Russian); English transl.: Siberian Adv. Math., 7 (1997), 5-17.
[4] T. Carleman, Sur lesequations integrales singulieres a noyau reel et symetrique, 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), 197254.
[7] N. I. Akhiezer, Integral operators with Carleman kernels, Uspekhi Mat. Nauk., 2:5 (1947), 93132 (in Russian).
[8] N. I. Akhiezer, I. M. Glazman, Theory of linear operators in Hilbert space, Nauka, Moscow, 1966 (in Russian); English transl. from the 3rd Russian ed.: Monographs and Studies in Mathematics, 9, 10, Pitman Advanced Publishing Program, Boston, 1981.
[9] C.G. Costley, On singular normal linear equations, Can. Math. Bull., 13 (1970), 199203.
[10] J. W. Williams, Linear integral equations with singular normal kernels of class I, J. Math. Anal. Appl., 68:2 (1979), 567579.
[11] V.B. Korotkov, Integral operators, Nauka, Novosibirsk, 1983 (in Russian).
[12] T. Kato, Perturbation theory for linear operators, Corr. print. of the 2nd ed., Springer-Verlag, Berlin-Heidelberg-New York, 1980.
[13] E. Hille, Functional analysis and semi-groups, Amer. Math. Soc. Colloq. Publ. 31, New York, 1948.
[14] L.V. Kantorovich, G.P. Akilov, Functional analysis, 3rd ed., Nauka, Moscow, 1984 (in Russian); English transl.: Pergamon Press, Oxford-Elmsford-New York, 1982.
[15] P. Halmos, V. Sunder, Bounded integral operators on L2 spaces, Springer, Berlin, 1978.
[16] M. Reed, B. Simon, Methods of modern mathematical physics. I. Functional analysis, rev. ed., Academic Press, San Diego, 1980.
[17] B. Misra, D. Speiser, G. Targonski, Integral operators in the theory of scattering, Helv. Phys. Acta, 36 (1963), 963980.
[18] A. C. Zaanen, An extension of Mercers theorem on continuous kernels of positive type, Simon Stevin, 29 (1952), 113124.
[19] J. Buescu, Positive integral operators in unbounded domains, J. Math. Anal. Appl., 296:1 (2004), 244255.
[20] I.M. Novitskii, Unitary equivalence between linear operators and integral operators with smooth kernels, Differentsialnye Uravneniya, 28:9 (1992), 16081616 (in Russian); English transl.: Differential Equations, 28:9 (1992), 1329-1337.
[21] I.M. Novitskii, Reduction of linear operators in L2 to integral form with smooth kernels, Dokl. Akad. Nauk SSSR, 318:5 (1991), 10881091 (in Russian); English transl.: Soviet Math. Dokl., 43:3 (1991), 874-877.
[22] I.M. Novitskii, Integral representations of linear operators by smooth Carleman kernels of Mercer type, Proc. Lond. Math. Soc. (3), 68:1 (1994), 161177.
[23] T. Carleman, Zur Theorie der linearen Integralgleichungen, Math. Z., 9 (1921), 196217.
[24] S.G. Mikhlin, On the convergence of Fredholm series, Doklady AN SSSR, XLII:9 (1944), 374377 (in Russian).
[25] F. Smithies, The Fredholm theory of integral equations, Duke Math. J., 8 (1941), 107130.