@article{TIMM_2005_11_1_a3,
author = {V. D. Batukhtin and S. I. Bigil'deev},
title = {Inheritance of the differential properties of potentials by functions},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {32--42},
year = {2005},
volume = {11},
number = {1},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2005_11_1_a3/}
}
TY - JOUR AU - V. D. Batukhtin AU - S. I. Bigil'deev TI - Inheritance of the differential properties of potentials by functions JO - Trudy Instituta matematiki i mehaniki PY - 2005 SP - 32 EP - 42 VL - 11 IS - 1 UR - http://geodesic.mathdoc.fr/item/TIMM_2005_11_1_a3/ LA - ru ID - TIMM_2005_11_1_a3 ER -
V. D. Batukhtin; S. I. Bigil'deev. Inheritance of the differential properties of potentials by functions. Trudy Instituta matematiki i mehaniki, Dynamical systems and control problems, Tome 11 (2005) no. 1, pp. 32-42. http://geodesic.mathdoc.fr/item/TIMM_2005_11_1_a3/
[1] Batukhtin V. D., Maiboroda L. A., Razryvnye ekstremalnye zadachi, Gippokrat, S.-P., 1995
[2] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 | MR | Zbl
[3] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1984 | MR | Zbl
[4] Batukhtin V. D., Bigildeev S. I., Bigildeeva T. B., “Optimizatsiya summiruemykh funktsii”, Kibernetika i sistemnyi analiz, 2002, no. 3, 73–89 | MR | Zbl
[5] Bigildeev S. I., Rolschikov V. E., “Svoistva approksimatsionnogo gradienta v zavisimosti ot vesovoi funktsii”, Izv. RAN. Teoriya i sistemy upravleniya, 1997, no. 4, 89–94 | MR
[6] Klark F., Optimizatsiya i negladkii analiz, Nauka, M., 1988 | MR | Zbl
[7] Bigildeev S. I., “Approksimatsionnaya proizvodnaya kak mnogoznachnoe otobrazhenie”, Vestn. Chelyabinskogo gos. un-ta, 1996, no. 1(3), 21–33 | MR
[8] Batukhtin V. D., Bigil'deev S. I., Bigil'deeva T. B., “Approximate gradient methods and the necessary conditions for the extremum of discontinuous functions”, Nonsmooth and discontinuous problems of control and optimization, Proceeding of the IFAC Workshop (NDPCO'98) (Chelyabinsk, June 17–20, 1998), eds. V. D. Batukhtin, F. M. Kirillova and V. I. Ukhobotov, Published for the International Federation of Automatic Control (IFAC),, Laxenburg, 1999, 25–34 | MR
[9] Bigildeev S. I., “Suschestvennaya optimizatsiya funktsii”, Optimizatsiya chislennykh metodov, Trudy mezhdunarodnoi nauchnoi konferentsii “Optimizatsiya chislennykh metodov”, posvyaschennoi 90-letiyu so dnya rozhdeniya S. L. Soboleva (1908–1989). Chast 1, ed. M. D. Ramazanov, IMVTs UNTs RAN, Ufa, 2000, 40–49
[10] Bigildeev S. I., “Optimizatsiya regulyarno approksimiruemykh funktsii”, Zhurnal na elektronnykh nositelyakh “Izvestiya Chelyabinskogo nauchnogo tsentra”, 2001, no. 3(12)
[11] Stein I. M., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR
[12] Stein E. M., Weiss G., Introduction to Fourier analysis on Euclidean spaces, Princeton, 1971 | MR
[13] Mysovskikh I. P., Interpolyatsionnye kubaturnye formuly, Nauka, M., 1981 | MR | Zbl
[14] Riss F., Sekefalvi-Nad B., Lektsii po funktsionalnomu analizu, Mir, M., 1979 | MR
[15] Calderon A. P., Zygmund A., “Local properties of solutions of elliptic partial differential equations”, Studia Math., 20 (1961), 171–225 | MR | Zbl
[16] Saks S., Teoriya integrala, IL, M., 1949
[17] Riesz M., “L'integrale de Riemann–Liouville et le probleme de Cauchy”, Acta Math., 81 (1949), 1–233 | DOI | MR
[18] Weyl H., “Bemerkungen zum Begriff der Differentialquotienten gebrochener Ordnung”, Zurich Natur. Gesellschaft, 62 (1917), 296–302 | Zbl
[19] Aronszajn N., Smith K. T., “Theory of Bessel potentials. I”, Ann. Inst. Fourier, 11 (1961), 385–475 | MR | Zbl