Gaussian Measures in Banach Spaces

1975 ◽  
Author(s):  
Hui-Hsiung Kuo
Keyword(s):  
Banach Spaces ◽  
Gaussian Measures

scholarly journals Karhunen–Loève decomposition of Gaussian measures on Banach spaces

2019 ◽  
Vol 39 (2) ◽  
pp. 279-297
Author(s):  
Xavier Bay ◽  
Jean-Charles Croix
Keyword(s):  
Brownian Motion ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Applied Mathematics ◽  
Canonical Decomposition ◽  
Spectral Theorem ◽  
Gaussian Measures ◽  
Covariance Operators ◽  
Active Interest ◽  
Special Case

The study of Gaussian measures on Banach spaces is of active interest both in pure and applied mathematics. In particular, the spectral theorem for self-adjoint compact operators on Hilbert spaces provides a canonical decomposition of Gaussian measures on Hilbert spaces, the socalled Karhunen–Ločve expansion. In this paper, we extend this result to Gaussian measures on Banach spaces in a very similar and constructive manner. In some sense, this can also be seen as a generalization of the spectral theorem for covariance operators associated with Gaussian measures on Banach spaces. In the special case of the standardWiener measure, this decomposition matches with Lévy–Ciesielski construction of Brownian motion.

Invariant Gaussian measures for operators on Banach spaces and linear dynamics

2006 ◽  
Vol 94 (1) ◽  
pp. 181-210 ◽  
Author(s):  
Frédéric Bayart ◽  
Sophie Grivaux
Keyword(s):  
Banach Spaces ◽  
Gaussian Measures ◽  
Linear Dynamics

The Support of Gaussian Measures on Banach Spaces

1973 ◽  
Vol 17 (4) ◽  
pp. 728-734 ◽  
Author(s):  
Balram S. Rajput
Keyword(s):  
Banach Spaces ◽  
Gaussian Measures

scholarly journals A characterization of Gaussian measures on Banach spaces

1977 ◽  
Vol 59 (3) ◽  
pp. 275-281
Author(s):  
K. Urbanik
Keyword(s):  
Banach Spaces ◽  
Gaussian Measures

Characterization of Certain Classes of Banach Spaces by Properties of Gaussian Measures

1980 ◽  
Vol 25 (1) ◽  
pp. 159-164 ◽  
Author(s):  
V. Linde ◽  
V. I. Tarieladze ◽  
S. A. Chobanyan
Keyword(s):  
Banach Spaces ◽  
Gaussian Measures
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