Geodesic
The Newton–Leibniz formula on Banach spaces and approximation of functions of an infinite-dimensional argument
Izvestiya. Mathematics, Tome 30 (1988) no. 1, pp. 145-161 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Properties of integrals over infinite-dimensional nonlinear manifolds are analyzed. A certain double averaging operation is introduced for functions on abstract separable Banach spaces; this operation leads to uniform approximation by smooth (in the Fréchet sense) functions in the case of spaces (and certain other cases). Bibliography: 10 titles. 
@article{IM2_1988_30_1_a7,
     author = {A. V. Uglanov},
     title = {The {Newton{\textendash}Leibniz} formula on {Banach} spaces and approximation of functions of an infinite-dimensional argument},
     journal = {Izvestiya. Mathematics},
     pages = {145--161},
     year = {1988},
     volume = {30},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1988_30_1_a7/}
}
TY  - JOUR
AU  - A. V. Uglanov
TI  - The Newton–Leibniz formula on Banach spaces and approximation of functions of an infinite-dimensional argument
JO  - Izvestiya. Mathematics
PY  - 1988
SP  - 145
EP  - 161
VL  - 30
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IM2_1988_30_1_a7/
LA  - en
ID  - IM2_1988_30_1_a7
ER  - 
%0 Journal Article
%A A. V. Uglanov
%T The Newton–Leibniz formula on Banach spaces and approximation of functions of an infinite-dimensional argument
%J Izvestiya. Mathematics
%D 1988
%P 145-161
%V 30
%N 1
%U http://geodesic.mathdoc.fr/item/IM2_1988_30_1_a7/
%G en
%F IM2_1988_30_1_a7
A. V. Uglanov. The Newton–Leibniz formula on Banach spaces and approximation of functions of an infinite-dimensional argument. Izvestiya. Mathematics, Tome 30 (1988) no. 1, pp. 145-161. http://geodesic.mathdoc.fr/item/IM2_1988_30_1_a7/

[1] Daletskii Yu. L., Fomin S. V., Mery i differentsialnye uravneniya v beskonechnomernykh prostranstvakh, Nauka, M., 1975, 384 pp. | MR

[2] Uglanov A. V., “Poverkhnostnye integraly v banakhovom prostranstve”, Matem. sb., 110:2 (1979), 189–217 | MR | Zbl

[3] Neve Zh., Matematicheskie osnovy teorii veroyatnostei, Mir, M., 1969, 310 pp. | MR | Zbl

[4] Efimova E. I., Uglanov A. V., “Formuly vektornogo analiza na banakhovom prostranstve”, Dokl. AN SSSR, 271:6 (1983), 1302–1306 | MR

[5] Uglanov A. V., “Odin rezultat o differentsiruemykh merakh na lineinom prostranstve”, Matem. ob., 100:2 (1976), 242–247 | MR | Zbl

[6] Uglanov A. V., “Parabolicheskie differentsialnye uravneniya vtorogo poryadka dlya obobschennykh mer na gilbertovom prostranstve”, Vestn. MGU, matem.-mekhan., 1978, no. 1, 16–22 | MR | Zbl

[7] Go Kh.-S., Gaussovskie mery v banakhovykh prostranstvakh, Mir, M., 1979, 175 pp.

[8] Edvards R. E., Funktsionalnyi analiz, Mir, M., 1969, 1071 pp.

[9] Bonic R., Frampton J., “Differentiable functions on certain Banach spaces”, Bull. Amer. Math. Soc., 71:2 (1965), 393–395 | DOI | MR | Zbl

[10] Uglanov A. V., “O delenii obobschennykh funktsii beskonechnogo chisla peremennykh na mnogochleny”, Dokl. AN SSSR, 264:5 (1982), 1096–1099 | MR | Zbl