A Karhunen-Lo\`{e}ve Theorem for Random Flows in Hilbert spaces
arXiv (Cornell University)(2023)
摘要
We develop a generalisation of Mercer's theorem to operator-valued kernels in infinite dimensional Hilbert spaces. We then apply our result to deduce a Karhunen-Lo\`eve theorem, valid for mean-square continuous Hilbertian functional data, i.e. flows in Hilbert spaces. That is, we prove a series expansion with uncorrelated coefficients for square-integrable random flows in a Hilbert space, that holds uniformly over time.
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关键词
random flows,theorem,karhunen-lo\`
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