Distributions and Analytical Measures on Infinite-Dimensional Spaces

被引：0

作者：

Belyaev, A. A. ^{[1
]}

Smolyanov, O. G. ^{[2
,3
]}

机构：

[1] Financial Univ Govt Russian Federat, Moscow 125993, Russia

[2] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow 119991, Russia

[3] State Univ, Moscow Inst Phys & Technol, Dolgoprudnyi 141700, Moscow Oblast, Russia

来源：

DOKLADY MATHEMATICS | 2018年 / 98卷 / 03期

关键词：

EQUATIONS;

D O I：

10.1134/S1064562418070013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 D and 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.

引用

页码：541 / 544

页数：4

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