Distributions and Analytical Measures on Infinite-Dimensional Spaces
- 作者: Belyaev A.1, Smolyanov O.2,3
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隶属关系:
- Financial University under the Government of the Russian Federation
- Faculty of Mechanics and Mathematics
- Moscow Institute of Physics and Technology (State University)
- 期: 卷 98, 编号 3 (2018)
- 页面: 541-544
- 栏目: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225576
- DOI: https://doi.org/10.1134/S1064562418070013
- ID: 225576
如何引用文章
详细
Spaces of test functions and spaces of distributions (generalized measures) on infinite-dimensional spaces are constructed, which, in the finite-dimensional case, coincide with classical spaces \(\mathscr{D}\) and \(\mathscr{D}'\). These distribution spaces contain generalized Feynman measures (but do not contain a generalized Lebesgue measure, which is not considered in this paper). For broad classes of infinite-dimensional differential equations in distribution spaces, the Cauchy problem has fundamental solutions. These results are much more definitive than those of A.Yu. Khrennikov’s and A.V. Uglanov’s pioneering works.
作者简介
A. Belyaev
Financial University under the Government of the Russian Federation
编辑信件的主要联系方式.
Email: AABelyaev@fa.ru
俄罗斯联邦, Moscow, 125993
O. Smolyanov
Faculty of Mechanics and Mathematics; Moscow Institute of Physics and Technology (State University)
Email: AABelyaev@fa.ru
俄罗斯联邦, Moscow, 119991; Dolgoprudnyi, Moscow oblast, 141700