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- W3012532012 abstract "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 so-called Karhunen-L{o} eve 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 to Gaussian measures on Banach spaces. In the special case of the standard Wiener measure, this decomposition matches with Paul L{e}vy's construction of Brownian motion." @default.
- W3012532012 created "2020-03-23" @default.
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- W3012532012 date "2017-04-05" @default.
- W3012532012 modified "2023-09-23" @default.
- W3012532012 title "Karhunen-Lo`eve decomposition of Gaussian measures on Banach spaces" @default.
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