Dynamical generalized functions and the multiplication problem
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2007), pp. 33-45.

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V. Ya. Derr; D. M. Kinzebulatov. Dynamical generalized functions and the multiplication problem. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2007), pp. 33-45. http://geodesic.mathdoc.fr/item/IVM_2007_5_a3/

[1] Dykhta V. A., Samsonyuk O. N., Optimalnoe impulsnoe upravlenie s prilozheniyami, Fizmatlit, M., 2003, 255 pp. | MR | Zbl

[2] Derr V. Ya., “K opredeleniyu ponyatiya resheniya differentsialnogo uravneniya s obobschennymi funktsiyami”, DAN SSSR, 298:2 (1988), 269–272 | MR | Zbl

[3] Sesekin A. N., “O nelineinykh differentsialnykh uravneniyakh v klassakh funktsii ogranichennoi variatsii”, Differents. uravneniya, 25:11 (1989), 1925–1932 | MR | Zbl

[4] Zavalischin S. T., Sesekin A. N., Impulsnye protsessy: modeli i prilozheniya, Nauka, M., 1991, 256 pp. | MR

[5] Miller B. M., “Method of discontinuous time change in problems of control for impulse and discrete continuous systems”, Automat. Remote Control, 54 (1993), 1727–1750 | MR | Zbl

[6] Vinter R. B., Pereira F. M. F. L., “A maximum principle for optimal processes with discontinuous trajectories”, SIAM J. Control and Optim., 26 (1988), 205–229 | DOI | MR | Zbl

[7] Motta M., Rampazzo F., “Dynamic programming for nonlinear systems driven by ordinary and impulsive controls”, SIAM J. Contr. and Optim., 34 (1996), 199–225 | DOI | MR | Zbl

[8] Silva G. N., Vinter R. B., “Necessary optimality conditions for optimal impulsive control problem”, SIAM J. Contr. and Optim., 35 (1997), 1829–1846 | DOI | MR | Zbl

[9] Colombeau J.-F., Elementary introduction to new generalized functions, North-Holland Publishing Co., Amsterdam, 1985, 281 pp. | MR | Zbl

[10] Bagarello F., “Multiplication of distributions in one dimension: possible approaches and applications to delta-function and its derivatives”, J. Math. Anal. Appl., 196 (1995), 885–901 | DOI | MR | Zbl

[11] Sarrico C. O. R., “Some distributional products with relativistic invariance”, Portugal Math., 51 (1994), 283–290 | MR | Zbl

[12] Bagarello F., “Multiplication of distributions in one dimension and first application to quantum field theory”, J. Math. Anal. Appl., 266 (2002), 298–320 | DOI | MR | Zbl

[13] Boman J., Kurasov P., “Finite rank singular pertrubations and distributions with discontinuous test functions”, Proc. Amer. Math. Soc., 126 (1998), 1673–1683 | DOI | MR | Zbl

[14] Shilov G. E., Matematicheskii analiz. Vtoroi spetsialnyi kurs, Izd-vo MGU, M., 1984, 207 pp. | MR | Zbl

[15] Vladimirov V. S., Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979, 318 pp. | MR

[16] Derr V. Ya., Dizendorf K. I., “O differentsialnykh uravneniyakh v $C$-obobschennykh funktsiyakh”, Izv. vuzov. Matematika, 1996, no. 11, 39–49 | MR | Zbl

[17] Sarrico C. O. R., “The linear Cauchy problem for a class of differential equations with distributional coefficients”, Portugal Math., 52 (1995), 379–390 | MR | Zbl

[18] Filippov A. F., Differentsialnye uravneniya s razryvnoi pravoi chastyu, Nauka, M., 1985, 224 pp. | MR

[19] Derr V. Ya., Kinzebulatov D. M., “Differentsialnye uravneniya s obobschennymi funktsiyami, dopuskayuschimi umnozhenie na razryvnye funktsii”, Vestn. Udmurtsk. un-ta, 2005, no. 1, 35–58

[20] Rishel R. W., “An extended Pontryagin principle for control systems whose control laws contain measures”, SIAM J. Control and Optim., 3 (1965), 191–205 | MR | Zbl

[21] Honig C. S., Volterra–Stieltjes integral equations, Mathematical Studies, 16, North Holland, Amsterdam, 1975, 152 pp. | MR

[22] Derr V. Ya., “Ob odnom obobschenii integrala Rimana–Stiltesa”, Izv. in-ta matem. i inform. UdGU, no. 3, Izhevsk, 1997, 3–29

[23] Derr V. Ja., “A generalization of Riemann–Stieltjes integral”, Functional Differential Equations, 9:3–4 (2002), 325–341 | MR | Zbl

[24] Derr V. Ya., Kinzebulatov D. M., “Alfa-integral tipa Stiltesa”, Vestn. Udmurtsk. un-ta, 2006, no. 1, 41–65

[25] Iosida K., Funktsionalnyi analiz, Mir, M., 1967, 624 pp. | MR

[26] Kurasov P., “Distributions theory with discontinuous test functions and differential operators with generalized coefficients”, J. Math. Anal. Appl., 201 (1996), 297–323 | DOI | MR | Zbl

[27] Tvrdy M., “Differential and integral equations with regulated solutions”, Equam, Praha, 1993, 1–104 | MR