Geodesic
On the space of regular smooth functions
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2011), pp. 87-98 Cet article a éte moissonné depuis la source Math-Net.Ru

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The concept of regular smooth function is defined. Any piecewise smooth function is regular smooth function, and any regular smooth function is Lipschitzian. Any regular smooth function has finite one-sided derivatives: the left-side derivative is continuous at the left and the right-side derivative is continuous on the right. One-sided derivatives generate concept of a regular derivative. The space of regular smooth functions is the closureof the space of piecewise linear functions on norm of space Lipschitzian functions. The space of piecewise smooth functions is everywhere dense in space of regular smooth functions. The analogue of the equation of Euler for the elementary variational problem in space of regular smooth functions is proved.
Keywords: one-sided derivative, piecewise smooth function, Lipschitzian function, regulated function
Mots-clés : calculus of variations. 
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V. I. Rodionov. On the space of regular smooth functions. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 1 (2011), pp. 87-98. http://geodesic.mathdoc.fr/item/VUU_2011_1_a8/

[1] Honig Ch. S., Volterra–Stieltjes integral equations, Mathematics Studies, 16, North-Holland, Amsterdam, 1975, 152 pp. | MR | Zbl

[2] Tvrdy M., “Regulated functions and the Perron–Stieltjes integral”, Casopis Pest. Mat., 1989, no. 114, 187–209 | MR | Zbl

[3] Rodionov V. I., “Ob odnom semeistve podprostranstv prostranstva preryvistykh funktsii”, Vestnik Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2009, no. 4, 7–24

[4] Rudin U., Funktsionalnyi analiz, Mir, M., 1975, 448 pp. | MR

[5] Rodionov V. I., “O prostranstve regulyarno differentsiruemykh funktsii”, Izvestiya Instituta matematiki i informatiki (UdGU), 2004, no. 1(29), 3–32

[6] Romanov E. L., “O zamykanii prostranstva splainov poryadka $m$ po spetsialnoi norme”, Vestnik Udmurtskogo universiteta. Matematika, 2006, no. 1, 107–110 | MR

[7] Alekseev V. M., Tikhomirov V. M., Fomin S. V., Optimalnoe upravlenie, Ucheb. posobie dlya vuzov, Nauka, M., 1979, 432 pp. | MR