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
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
收藏
页码:550 / 552
页数:3
相关论文
共 8 条
[1]  
[Anonymous], MATEM ZAMET
[2]  
[Anonymous], USPEKHI MAT NAUK
[3]  
Bogachev V.I, 2006, Measure Theory, VII
[4]  
Bogachev V. I., 2011, Real and Functional Analysis: University Course
[5]  
GUERQUIN M, 1973, COLLOQ MATH, V28, P145
[6]  
Kuo H. H., 1975, GAUSSIAN MEASURES BA
[7]  
Smolyanov O.G., 2015, Path Integrals
[8]  
SMOLYANOV OG, 1983, VESTN MOSK U MAT M+, V38, P1