Linear Volterra operators in some metric spaces
Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 26 (2007) no. 26, pp. 223-240
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E. Litsin. Linear Volterra operators in some metric spaces. Trudy Seminara im. I.G. Petrovskogo, Trudy Seminara imeni I. G. Petrovskogo, Tome 26 (2007) no. 26, pp. 223-240. http://geodesic.mathdoc.fr/item/TSP_2007_26_26_a9/

[1] And\^{o T.}, “Positive linear operators in semi-ordered linear spaces”, J. Fac. Sci. Hokkaido Univ. Ser. 1, 1957, no. 13, 214–228 | MR | Zbl

[2] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Vvedenie v teoriyu funktsionalno-differentsialnykh uravnenii, Nauka, M., 1991 | MR | Zbl

[3] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Elementy sovremennoi teorii funktsionalno-differentsialnykh uravnenii. Metody i prilozheniya, IKT, M., 2002

[4] Bainov D. D., Myshkis A. D., Zahariev A. I., “On an abstract analog of the Bellman–Gronwall inequality”, Publ. RIMS, Kyoto Univ., 20:5 (1984), 903–911 | DOI | MR | Zbl

[5] Bukhgeim A. L., Uravneniya Volterra i obratnye zadachi, Nauka, Novosibirsk, 1983 | MR

[6] Cinquini S., “Sulle equazioni funzionali del tipo di Volterra”, Rend. Accad. Naz. Lincei., 17 (1983), 616–621

[7] Corduneanu C., Integral Equations and Applications, Cambridge Univ. Press, Cambridge, 1991 | MR | Zbl

[8] Drakhlin M. E., Ponosov A., Stepanov E., “On some classes of operators determined by the structure of their memory”, Proc. Edinburgh Math. Soc., 45:2 (2002), 467–490 | DOI | MR | Zbl

[9] Drakhlin M. E., Litsyn E., Ponosov A., Stepanov E., “Generalizing the property of locality: atomic/coatomic operators and applications”, JNCA, 7:2 (2006), 139–162 | MR | Zbl

[10] Drakhlin M. E., Litsyn E., “On the memory of atomic operators”, JNCA, 6:2 (2005), 235–249 | MR | Zbl

[11] Drakhlin M. E., Litsyn E., “Volterra operator: Back to the future”, JNCA, 6:3 (2005), 375–391 | MR | Zbl

[12] Feintuch A., Saeks R., System theory. A Hilbert space approach, Acad. Press, New York, 1982 | MR | Zbl

[13] Gokhberg I. Ts., Krein M. G., Teoriya volterrovykh operatorov v gilbertovykh prostranstvakh i ee prilozheniya, Nauka, M., 1967

[14] Graffi D., “Sopra una equazione funzionali e la sua applicazione a un problema di fisica ereditaria”, Ann. Mat. Pura Appl., 9 (1931), 143–179 | DOI | MR

[15] Gusarenko S. A., “Ob odnom obobschenii ponyatiya volterrovogo operatora”, DAN SSSR, 295:5 (1987), 1046–1049 | MR | Zbl

[16] Guryanova I. E., Myshkis A. D., “O neprodolzhimykh resheniyakh abstraktnykh integralnykh uravnenii tipa Volterra”, Differents. uravneniya, 22:10 (1986), 1786–1789 | MR | Zbl

[17] Kurbatov V. G., “Lineinye funktsionalno-differentsialnye uravneniya neitralnogo tipa i zapazdyvayuschii spektr”, Sib. mat. zhurn., 16:3 (1975), 538–550 | MR

[18] Kurbatov V. G., Lineinye differentsialno-raznostnye uravneniya, Izd-vo VGU, Voronezh, 1990 | MR | Zbl

[19] Litsyna E. M., “Ob obschei teorii funktsionalno-differentsialnykh uravnenii”, Differents. uravneniya, 24:6 (1988), 977–986 | MR

[20] Myshkis A. D., Lineinye differentsialnye uravneniya s zapazdyvayuschim argumentom, Nauka, M., 1972 | MR | Zbl

[21] Sikorski R., Boolean algeras, Springer, Berlin, 1960 | MR | Zbl

[22] Sumin V. I., “Funktsionalno-operatornye volterrovy uravneniya v teorii optimalnogo upravleniya raspredelennymi sistemami”, DAN SSSR, 305:5 (1989), 1056–1059 | MR | Zbl

[23] Sumin V. I., “Funktsionalnye volterrovy operatory v teorii optimalnogo upravleniya raspredelennymi sistemami. I”, Uravnenie Volterra i upravlyaemye nachalno-kraevye zadachi, Izd-vo Nizhegorodskogo un-ta, N. Novgorod, 1992

[24] Sumin V. I., Chernov A. V., “Operatory v prostranstvakh izmerimykh funktsii: svoistvo volterrovosti i kvazinilpotentnost”, Differents. uravneniya, 34:10 (1998), 1402–1411 | MR | Zbl

[25] Tikhonov A. N., “O funktsionalnykh uravneniyakh tipa Volterra i ikh primeneniyakh k nekotorym zadacham matematicheskoi fiziki”, Byul. MGU, 1, sektsiya A:8 (1938), 1–25 | MR

[26] Tonelli L., “Sulle equazioni funzionali del tipo di Volterra”, Bull. Calcula Math. Soc., 20 (1929), 31–48; Opere Scelte 4, 198–212

[27] Youla D. C., Carlin H. I., Castriota L. J., “Bounded real scattering matrices and the foundations of linear passive network theory”, IRE Trans. Circuit Theory, CT-6 (1959), 102–124 | DOI

[28] V\^{ath M.}, “Abstract Voltrerra equations of the second kind”, J. Integral Equations Appl., 10:9 (1998), 125–144 | MR

[29] Volterra V., Leçons sur les équations integrales et les équations integro-differentielles, Paris, 1913

[30] Zabreiko P. P., “Ob integralnykh operatorakh Volterra”, Uspekhi mat. nauk, 22:1 (1967), 167–168 | MR

[31] Zabreiko P. P., “O spektralnom radiuse integralnykh operatorov Volterra”, Lit. mat. sb., 7:2 (1967), 281–287 | MR

[32] Zhukovskii E. S., “K teorii uravnenii Volterra”, Differents. uravneniya, 25:9 (1989), 1599–1605 | MR

[33] Zhukovskii E. S., “Volterrovost i spektralnye svoistva operatora vnutrennei superpozitsii”, Differents. uravneniya, 30:2 (1994), 250–255 | MR