Hilbert supports of measures on locally convex spaces

被引：3

作者：

Smolyanova, M. O. ^{[1
]}

机构：

[1] Russian Acad Sci, Steklov Math Inst, Moscow 119991, Russia

来源：

RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS | 2015年 / 22卷 / 04期

关键词：

Hilbert Space; Dual Space; Convex Space; Gaussian Measure; Separable Hilbert Space;

D O I：

10.1134/S1061920815040159

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In the paper, we discuss relationships between the existence of Hilbert supports of countably additive measures on a locally convex space (LCS) and the continuity of their Fourier transforms in the Gross-Sazonov topology (which is defined below) on the dual space. In particular, it follows from the theorem proved in the paper that the Fourier transform of the Wiener measure on C[0, 1] is not continuous in the Gross-Sazonov topology on the dual space endowed with the Mackey topology (the strongest locally convex topology among those consistent with the duality between and C[0, 1]).

引用

页码：550 / 552

页数：3