On a probabilistic approximation of a group of unitary operators
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 32, Tome 510 (2022), pp. 211-224 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We construct a probabilistic approximation of the Cauchy problem solution for a high-order Schrödinger equation with bounded potential in the form of expectations of functionals of a point random field.
@article{ZNSL_2022_510_a12,
     author = {M. V. Platonova},
     title = {On a probabilistic approximation of a group of unitary operators},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {211--224},
     year = {2022},
     volume = {510},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_510_a12/}
}
TY  - JOUR
AU  - M. V. Platonova
TI  - On a probabilistic approximation of a group of unitary operators
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2022
SP  - 211
EP  - 224
VL  - 510
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2022_510_a12/
LA  - ru
ID  - ZNSL_2022_510_a12
ER  - 
%0 Journal Article
%A M. V. Platonova
%T On a probabilistic approximation of a group of unitary operators
%J Zapiski Nauchnykh Seminarov POMI
%D 2022
%P 211-224
%V 510
%U http://geodesic.mathdoc.fr/item/ZNSL_2022_510_a12/
%G ru
%F ZNSL_2022_510_a12
M. V. Platonova. On a probabilistic approximation of a group of unitary operators. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 32, Tome 510 (2022), pp. 211-224. http://geodesic.mathdoc.fr/item/ZNSL_2022_510_a12/

[1] Yu. L. Daletskii, S. V. Fomin, Mery i differentsialnye uravneniya v funktsionalnykh prostranstvakh, Nauka, M., 1983

[2] N. Danford, Dzh. Shvarts, Lineinye operatory. Obschaya teoriya, Izdatelstvo inostrannoi literatury, M., 1962

[3] I. A. Ibragimov, N. V. Smorodina, M. M. Faddeev, “Veroyatnostnaya approksimatsiya operatora evolyutsii”, Funkts. analiz i ego pril., 52:2 (2018), 25–39 | MR

[4] T. Kato, Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR

[5] Dzh. Kingman, Puassonovskie protsessy, MTsNMO, M., 2007

[6] M. V. Platonova, “Analog formuly Feinmana–Katsa dlya operatora vysokogo poryadka”, Teor. veroyatn. i ee primen., 67:1 (2022), 81–99

[7] M. V. Platonova, S.V. Tsykin, “Veroyatnostnaya approksimatsiya resheniya zadachi Koshi dlya uravneniya Shredingera vysokogo poryadka”, Teor. veroyatn. i ee primen., 65:4 (2020), 710–724 | MR

[8] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki, v. 1, Mir, M., 1977 | MR

[9] O. G. Smolyanov, E. T. Shavgulidze, Kontinualnye integraly, LENAND, M., 2015, 336 pp.