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RT @mathOCb: Yicun Zhen, Bertand Chapron: Bridging Koopman Operator with Hilbert-Schmidt Operator Associated to Stationary Time Series http…
semigroup $\{\mathcal{K}^s: s\geq 0\}$ is equivalent, almost surely, to the classical Koopman one-parameter semigroup defined on $L^2(X,\nu)$, if the dynamical system is ergodic and has invariant measure $\nu$ on the phase space $X$. [4/4 of https://t.co/C
$s\geq 0$. Let $f = \displaystyle\sum_{i=1}^{\infty}a_iv_i + f^{\perp}$ be the orthogonal decomposition with descending $|a_i|$. We prove that $\displaystyle\lim_{\tau\to\infty}\lambda_{\tau,i} = |a_i|^2$. The continuous one-parameter [3/4 of https://t.co/