Cramér–Karhunen–Loève representation and harmonic principal component analysis of functional time series

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Dynamic functional principal components (2012, methodology): “The methodology relies on a frequency domain analysis for functional data: a topic which is still in its infancy (see, for instance, Panaretos and Tavakoli (2013a)).”
White Noise Testing and Model Diagnostic Checking for Functional Time Series (2016, methodology): “Our test is constructed based on the periodogram function recently X. Zhang / Journal of Econometrics 194 (2016) 76–95 77 introduced by Panaretos and Tavakoli (2013a) and it has nontrivial power against Pitman’s local alternatives that are within a √ T - neighborhood of the null hypothesis, where T…”
Fourier analysis of stationary time series in function space (2013, methodology): “Remark F.16 in the supplementary material [Panaretos and Tavakoli (2013)] tells us that the convergence of the convolution integral depends on the uniform continuity parameter δ(ε), which here will depend on the size of the sampling grid M =M(T ); in other words, δ(ε) = δ(ε,M).”