The Experts below are selected from a list of 9489 Experts worldwide ranked by ideXlab platform
François Roueff - One of the best experts on this subject based on the ideXlab platform.
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Spectral analysis of weakly stationary processes valued in a Separable Hilbert Space
2020Co-Authors: Amaury Durand, François RoueffAbstract:In this paper, we review and clarify the construction of a spectral theory for weakly-stationary processes valued in a Separable Hilbert Space. We introduce the basic fundamental concepts and results of functional analysis and operator theory needed to follow the way paved by Payen in [52], Mandrekar and Salehi in [45] and Kakihara in [33]. They lead us to view the spectral representation of a weakly stationary Hilbert valued time series as a gramian isometry between its time domain and its spectral domain. Time invariant linear filters with Hilbert-valued inputs and outputs are then defined through their operator transfer functions in the spectral domain. General results on the composition and inversion of such filters follow naturally. Spectral representations have enjoyed a renewed interest in the context of functional time series. The gramian isometry between the time and spectral domains constitutes an interesting and enlightening complement to recent approaches such as the one proposed in [50]. We also provide an overview of recent statistical results for the spectral analysis of functional time-series.
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Spectral representations of weakly stationary processes valued in a Separable Hilbert Space : a survey with applications on functional time series
arXiv: Statistics Theory, 2019Co-Authors: Amaury Durand, François RoueffAbstract:In this paper, we review and clarify the construction of a spectral theory for weakly-stationary processes valued in a Separable Hilbert Space. We emphasize the link with functional analysis and provide thorough discussions on the different approaches leading to fundamental results on representations in the spectral domain. The clearest and most complete way to view such representations relies on a Gramian isometry between the time domain and the spectral domain. This theory is particularly useful for modeling functional time series. In this context, we define time invariant operator-valued linear filters in the spectral domain and derive results on composition and inversion of such filters. The advantage of a spectral domain approach over a time domain approach is illustrated through the construction of a class of functional autoregressive fractionaly integrated moving average processes which extend the celebrated class of ARFIMA processes that have been widely and successfully used to model univariate time series. Such functional ARFIMA processes are natural counterparts to processes defined in the time domain that were previously introduced for modeling long range dependence in the context of functional time series.
Amaury Durand - One of the best experts on this subject based on the ideXlab platform.
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Spectral analysis of weakly stationary processes valued in a Separable Hilbert Space
2020Co-Authors: Amaury Durand, François RoueffAbstract:In this paper, we review and clarify the construction of a spectral theory for weakly-stationary processes valued in a Separable Hilbert Space. We introduce the basic fundamental concepts and results of functional analysis and operator theory needed to follow the way paved by Payen in [52], Mandrekar and Salehi in [45] and Kakihara in [33]. They lead us to view the spectral representation of a weakly stationary Hilbert valued time series as a gramian isometry between its time domain and its spectral domain. Time invariant linear filters with Hilbert-valued inputs and outputs are then defined through their operator transfer functions in the spectral domain. General results on the composition and inversion of such filters follow naturally. Spectral representations have enjoyed a renewed interest in the context of functional time series. The gramian isometry between the time and spectral domains constitutes an interesting and enlightening complement to recent approaches such as the one proposed in [50]. We also provide an overview of recent statistical results for the spectral analysis of functional time-series.
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Spectral representations of weakly stationary processes valued in a Separable Hilbert Space : a survey with applications on functional time series
arXiv: Statistics Theory, 2019Co-Authors: Amaury Durand, François RoueffAbstract:In this paper, we review and clarify the construction of a spectral theory for weakly-stationary processes valued in a Separable Hilbert Space. We emphasize the link with functional analysis and provide thorough discussions on the different approaches leading to fundamental results on representations in the spectral domain. The clearest and most complete way to view such representations relies on a Gramian isometry between the time domain and the spectral domain. This theory is particularly useful for modeling functional time series. In this context, we define time invariant operator-valued linear filters in the spectral domain and derive results on composition and inversion of such filters. The advantage of a spectral domain approach over a time domain approach is illustrated through the construction of a class of functional autoregressive fractionaly integrated moving average processes which extend the celebrated class of ARFIMA processes that have been widely and successfully used to model univariate time series. Such functional ARFIMA processes are natural counterparts to processes defined in the time domain that were previously introduced for modeling long range dependence in the context of functional time series.
E. R. Negrin - One of the best experts on this subject based on the ideXlab platform.
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Weighted Shift Operators Which are m-Isometries
Integral Equations and Operator Theory, 2010Co-Authors: Teresa Bermúdez, Antonio Martinón, E. R. NegrinAbstract:We give a characterization of m-isometric operators on a Separable Hilbert Space. Moreover, we characterize the unilateral weighted shift operators which are m-isometries.
Roland Girgensohn - One of the best experts on this subject based on the ideXlab platform.
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subdifferentials whose graphs are not norm x weak closed
Canadian Mathematical Bulletin, 2003Co-Authors: Jonathan M. Borwein, Simon Fitzpatrick, Roland GirgensohnAbstract:In this note we give examples of convex functions whose subdifferentials have unpleasant properties. Particularly, we exhibit a \pcf on Separable Hilbert Space such that the graph of its subdifferential is not closed in the product of the norm and bounded weak topologies. We also exhibit a set whose sequential normal cone is not norm closed.
L. Randriamihamison - One of the best experts on this subject based on the ideXlab platform.
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The spectrum of diagonal perturbation of weighted shift operator
arXiv: Functional Analysis, 2016Co-Authors: Mohamed Lamine Sahari, A. K. Taha, L. RandriamihamisonAbstract:This paper provides a description of the spectrum of diagonal perturbation of weighted shift operator acting on a Separable Hilbert Space.
