Strong-linear independence for differential images of Gauss potentials
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 3, pp. 273-279
Cet article a éte moissonné depuis la source Math-Net.Ru
J. С. Mairhuber theorem concerning the Chebyshev approximation problem provides a resolution uniqueness only for the case of one-dimensional compacts. In present paper an attempt to overcome the above restriction by means of stochastic interpretation applied to solvability is taken. In the context of such a position the multiparametric system of Gauss potentials is studied. The strong linear independence for potentials and its images resulting from the constant factors linear differential operator is proved. The differentially conditioned analytic function generating based on a linear combination of Gauss potentials is examined.
@article{SJVM_1999_2_3_a5,
author = {V. A. Leus},
title = {Strong-linear independence for differential images of {Gauss} potentials},
journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
pages = {273--279},
year = {1999},
volume = {2},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SJVM_1999_2_3_a5/}
}
V. A. Leus. Strong-linear independence for differential images of Gauss potentials. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 3, pp. 273-279. http://geodesic.mathdoc.fr/item/SJVM_1999_2_3_a5/
[1] Guster R. S., Kudryavtsev L. D., Levitan B. M., Elementy teorii funktsii, GIFML, M., 1963
[2] Leus V. A., “O differentsialno obuslovlennom generirovanii funktsii na baze stepennykh potentsialov”, Sib. zhurn. vychisl. matem. / RAN. Sib. otd-nie, 1:4 (1998), 363–371
[3] Vladimirov B. C., Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1976 | MR | Zbl
[4] Godunov S. K., Antonov A. G., Kirilyuk O. P., Kostin V. I., Garantirovannaya tochnost resheniya sistem lineinykh uravnenii v evklidovykh prostranstvakh, Nauka, Novosibirsk, 1992 | MR
[5] Ignatov M. I., Pevnyi A. B., Naturalnye splainy mnogikh peremennykh, Nauka, L., 1991 | MR | Zbl