Email this article Distributions and Analytical Measures on Infinite-Dimensional Spaces
- Authors: Belyaev A.A.1, Smolyanov O.G.2,3
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Affiliations:
- Financial University under the Government of the Russian Federation
- Faculty of Mechanics and Mathematics
- Moscow Institute of Physics and Technology (State University)
- Issue: Vol 98, No 3 (2018)
- Pages: 541-544
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225576
- DOI: https://doi.org/10.1134/S1064562418070013
- ID: 225576
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Abstract
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.
About the authors
A. A. Belyaev
Financial University under the Government of the Russian Federation
Author for correspondence.
Email: AABelyaev@fa.ru
Russian Federation, Moscow, 125993
O. G. Smolyanov
Faculty of Mechanics and Mathematics; Moscow Institute of Physics and Technology (State University)
Email: AABelyaev@fa.ru
Russian Federation, Moscow, 119991; Dolgoprudnyi, Moscow oblast, 141700
