Nonstandard analysis of linear and nonlinear operators
Vladikavkazskij matematičeskij žurnal, Tome 1 (1999) no. 1, pp. 30-36
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A. G. Kusraev. Nonstandard analysis of linear and nonlinear operators. Vladikavkazskij matematičeskij žurnal, Tome 1 (1999) no. 1, pp. 30-36. http://geodesic.mathdoc.fr/item/VMJ_1999_1_1_a2/

[1] Kusraev A. G., Kutateladze S. S., Nestandartnye metody analiza, Nauka, Novosibirsk, 1990 | MR

[2] Devis M., Prikladnoi nestandartnyi analiz, Mir, M., 1980 | MR

[3] Albeverio S. i dr., Nestandartnye metody v stokhasticheskom analize i matematicheskoi fizike, Mir, M., 1990 | MR | Zbl

[4] Hurd A.(ed.), Nonstandard Analysis. Recent Development, Springer, Berlin, 1983 | MR | Zbl

[5] Cutland N. (ed.), Nonstandard Analysis and its Applications, Cambridge Univ. Press, Cambridge, 1988 | MR | Zbl

[6] Takeuti G., Two Applications of Logics to Mathematics, Iwanami, Tokio; Princeton Univ. Press, Princeton, 1978 | MR | Zbl

[7] Stroyan K. D., Luxemburg W. A. J., Introduction to the Theory of Infinitesimals, Academic Press, N. Y. a.o., 1976 | MR | Zbl

[8] Moore L. C., “Hyperfinite extensions of bounded operators on a separable Hilbert space”, Trans. Amer. Math. Soc., 218 (1976), 285–295 | DOI | MR | Zbl

[9] Cutland N., “Nonstandart measure theory and its applications”, Bull. London Math. Soc., 15:6 (1983), 105–137 | DOI | MR

[10] Gordon E. I., “O merakh Lëba”, Izvestiya vuzov. Matematika, 1991, no. 2, 25–33 | MR | Zbl

[11] Kusraev A. G., “Poryadkovo nepreryvnye funktsionaly v bulevoznachnykh modelyakh teorii mnozhestv”, Sib. mat. zhurn., 25:1 (1984), 69–79 | MR | Zbl

[12] Kusraev A. G., Vektornaya dvoistvennost i ee prilozheniya, Nauka, Novosibirsk, 1985 | MR | Zbl

[13] Akilov G. P., Kolesnikov E. N., Kusraev A. G., “O lebegovom rasshirenii polozhitelnykh operatorov”, Dokl. AN SSSR, 300:5 (1988), 83–91 | MR

[14] Kusraev A. G., Malyugin S. A., Nekotorye voprosy teorii vektornykh mer, In-t mat-ki SO AN SSSR, Novosibirsk, 1988, 190 pp. | MR

[15] Kusraev A. G., Malyugin S. A., “Ob atomicheskom razlozhenii vektornykh mer”, Sib. mat. zhurn., 30:5 (1989), 101–110 | MR | Zbl

[16] Kutateladze S. S., “Variant nestandartnogo vypuklogo programmirovaniya”, Sib. mat. zhurn., 27:4 (1986), 84–92 | MR | Zbl

[17] Kusraev A. G., Kutateladze S. S., “O kombinirovanii nestandartnykh metodov”, Sib. mat. zhurn., 31:5 (1990), 69–78 | MR

[18] Kutateladze S. S., “Ob oskolkakh polozhitelnykh operatorov”, Sib. mat. zhurn., 30:5 (1989), 111–119 | MR | Zbl

[19] Gordon E. I., “Nestandartnye konechnomernye analogi operatorov v $L(R)$”, Sib. mat. zhurn., 29:2 (1988), 45–59 | MR | Zbl

[20] Gordon E. I., “O preobrazovanii Fure v nestandartnom analize”, Izvestiya vuzov. Matematika, 1989, no. 2, 17–25 | MR

[21] Gordon E. I., “Giperkonechnye approksimatsii lokalno kompaktnykh abelevykh grupp”, Dokl. AN SSSR, 314:5 (1990), 1044–1047 | MR | Zbl

[22] Gordon E. I., “Nestandartnyi analiz i kompaktnye abelevy gruppy”, Sib. mat. zhurn., 32:2 (1991), 26–40 | MR | Zbl

[23] Vershik A. M., “Schetnye gruppy, blizkie k konechnym”: Grinlif F., Invariantnye srednie na topologicheskikh gruppakh, Mir, M., 1973, 112–135

[24] Vershik A., “Amenability and approximation of infinite groups”, Sel. Math. sov., 2:4 (1982), 311–330 | MR | Zbl

[25] Van den Dries L., Wilkie A. J., “On Gromov's theorem concerning groups of polinomial grouth and elementary logic”, J. Algebra, 89:2 (1984), 349–374 | DOI | MR | Zbl

[26] Maharam D., “On positive operators”, Contemporary Math., 26 (1984), 263–277 | MR | Zbl

[27] Kusraev A. G., “O stroenii vektornykh mer i polnykh bulevykh algebr”, Dokl. AN SSSR, 318:6 (1991) | Zbl

[28] Gohberg I., Lancaster P., Rodman L., “Spectral analysis of selfajoint matrix polinomials”, Ann. Math. Ser. 2, 112:1 (1980), 33–71 | DOI | MR | Zbl

[29] Shaefer H. H., Banach Lattices and Positive Operators, Springer, Berlin a.o., 1974 | MR

[30] Keldysh M. V., “O polnote sobstvennykh funktsii nekotorykh klassov nesamosopryazhennykh operatorov”, Uspekhi mat. nauk, 26:4 (1971), 15–41 | MR | Zbl

[31] Mazon J. M., Sequra de Leon S., “Order bounded orthogonally additive operators”, Rev. Roum. Math. Pures Appl., 30:4 (1990), 329–354 | MR

[32] Arkeryd L., Bergh J., “Some properties of Loeb-Sobolev spaces”, J. London Math. Soc., 34:2 (1986), 317–334 | DOI | MR | Zbl

[33] Lyubetskii V. A., Gordon E. I., “Bulevy rasshireniya ravnomernykh struktur”, Issledovaniya po neklassicheskim logikam i formalnym sistemam, Nauka, M., 1983, 82–153 | MR