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arXiv · 2303.00702

A Karhunen-Lo\`{e}ve Theorem for Random Flows in Hilbert spaces

Leonardo V. Santoro·Kartik G. Waghmare·Victor M. Panaretos
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Abstract

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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Leonardo V. Santoro, Kartik G. Waghmare, Victor M. Panaretos. 2023-03-01. A Karhunen-Lo\`{e}ve Theorem for Random Flows in Hilbert spaces. https://arxiv.org/abs/2303.00702

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