I am a beginner. By asking this question, I means that, to construct a Hilbert space, should $\mathcal{X}$ satisfy some properties? Furthermore, in some papers especially on machine learning, statistic, and optimization, many problems are formulated on an observed finite data set $\mathcal{Z}$, and the final mathematical results lie in a Hilbert space (e.g., kernel regression), then how should I believe that $\mathcal{Z}$ is a subset of $\mathcal{X}$ ?
2026-03-29 22:41:16.1774824076
How to understand ' Let $\mathcal{H}$ be a Hilbert space of functions $f$ : $ \mathcal{X} \rightarrow R$, denoted on a non-empty set $\mathcal{X}$.'
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