Correction to: LRD spectral analysis of multifractional functional time series on manifolds

Correction to: TEST https://doi.org/10.1007/s11749-023-00913-7

In equation (3.7), the following post-publication correction consisting of interchanging the function exponents $L(\theta )$ and $l(\theta )$ in such an equation was necessary. Specifically, the correct expression of equation (3.7) of the article would be:

$$\begin{aligned}{} & {} \int _{-\pi }^{\pi } \left\| {\mathcal {F}}_{\omega }\right\| _{{\mathcal {S}}(L^{2}({\mathbb {M}}_{d},d\nu ; {\mathbb {C}}))}^{2}d\omega =\sum _{n\in {\mathbb {N}}_{0}}\delta (n,d)\int _{-\pi }^{\pi }|f_{n}(\omega )|^{2}d\omega \\{} & {} \quad \le \left\{ \left[ \int _{-\pi }^{-1}+\int _{1}^{\pi }\right] |\omega |^{-2l(\theta ) } + \int _{-1}^{1} |\omega |^{-2L(\theta ) }\right\} \left\| {\mathcal {M}}_{\omega }\right\| ^{2}_{{\mathcal {S}}\left( L^{2}({\mathbb {M}}_{d},d\nu ; {\mathbb {C}})\right) }d\omega <\infty . \end{aligned}$$