Search results for "Hilbert scale"

showing 2 items of 2 documents

Thresholding projection estimators in functional linear models

2008

We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows to get consistency under broad assumptions as well as minimax rates of convergence under additional regularity hypotheses. We also consider the particular case of Sobolev spaces generated by the trigonometric basis which permits to get easily mean squared error of prediction as well as estimators of the derivatives of the regression function. We prove these estimators are minimax and rates of convergence are given for some particular cases.

FOS: Computer and information sciencesStatistics and ProbabilityMathematical optimizationStatistics::TheoryMean squared error of predictionMean squared errorMathematics - Statistics TheoryStatistics Theory (math.ST)Projection (linear algebra)Methodology (stat.ME)FOS: MathematicsApplied mathematicsStatistics - MethodologyMathematicsLinear inverse problemNumerical AnalysisLinear modelEstimatorRegression analysisMinimaxSobolev spaceThresholdingOptimal rate of convergenceDerivatives estimationRate of convergenceHilbert scaleStatistics Probability and UncertaintyGalerkin methodJournal of Multivariate Analysis
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Banach partial *-algebras: an overview

2019

A Banach partial $*$-algebra is a locally convex partial $*$-algebra whose total space is a Banach space. A Banach partial $*$-algebra is said to be of type (B) if it possesses a generating family of multiplier spaces that are also Banach spaces. We describe the basic properties of these objects and display a number of examples, namely, $L^p$-like function spaces and spaces of operators on Hilbert scales or lattices. Finally we analyze the important cases of Banach quasi $*$-algebras and $CQ^*$-algebras.

Pure mathematicsMathematics::Functional AnalysisAlgebra and Number Theorypartial inner product spacesPartial *-algebra Banach partial *-algebra CQ*-algebra partial inner product space operators on Hilbert scale.Partial algebraPartial *-algebraspartial $*$-algebraCQ*-algebraspartial inner product spaceSettore MAT/05 - Analisi Matematica$CQ^*$-algebraBanach partial *-algebrasoperators on Hilbert scaleBanach partial $*$-algebra46J1008A55Analysis47L60Mathematics
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