Search results for "Multilinear map"

showing 5 items of 35 documents

Factorization of strongly (p,sigma)-continuous multilinear operators

2013

We introduce the new ideal of strongly-continuous linear operators in order to study the adjoints of the -absolutely continuous linear operators. Starting from this ideal we build a new multi-ideal by using the composition method. We prove the corresponding Pietsch domination theorem and we present a representation of this multi-ideal by a tensor norm. A factorization theorem characterizing the corresponding multi-ideal - which is also new for the linear case - is given. When applied to the case of the Cohen strongly -summing operators, this result gives also a new factorization theorem.

Unbounded operatorDiscrete mathematicsMultilinear mapPrimary 46A32Algebra and Number TheoryMathematics::Commutative AlgebraTensor normSpectral theoremOperator theoryPietsch domination theoremMultilinear operatorsymbols.namesakeFactorizationNorm (mathematics)Weierstrass factorization theoremsymbolsSecondary 47B10FactorizationMATEMATICA APLICADAOperator normAbsolutely continuous operatorsMathematics
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Some Non-linear Geometrical Properties of Banach Spaces

2014

In this survey we report on very recent results about some non-linear geometrical properties of many classes of real and complex Banach spaces and uniform algebras, including the ball algebra \(\fancyscript{A}_u(B_X)\) of all uniformly continuous functions on the closed unit ball and holomorphic on the open unit ball of a complex Banach space \(X\). These geometrical properties are: Polynomial numerical index, Polynomial Daugavet property and Bishop-Phelp-Bollobas property for multilinear mappings.

Unit sphereMathematics::Functional AnalysisNonlinear systemPure mathematicsUniform continuityMultilinear mapBanach spaceHolomorphic functionBall (mathematics)Disk algebraMathematics
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Multilinear Fourier multipliers related to time–frequency localization

2013

We consider multilinear multipliers associated in a natural way with localization operators. Boundedness and compactness results are obtained. In particular, we get a geometric condition on a subset A⊂R2d which guarantees that, for a fixed synthesis window ψ∈L2(Rd), the family of localization operators Lφ,ψA obtained when the analysis window φ varies on the unit ball of L2(Rd) is a relatively compact set of compact operators.

Unit sphereMultilinear mapApplied MathematicsMathematical analysisCompact operatorCompact operator on Hilbert spaceTime–frequency analysissymbols.namesakeFourier transformCompact spaceRelatively compact subspacesymbolsAnalysisMathematicsJournal of Mathematical Analysis and Applications
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QSPR with descriptors based on averages of vertex invariants. An artificial neural network study

2014

New type of indices, the mean molecular connectivity indices (MMCI), based on nine different concepts of mean are proposed to model, together with molecular connectivity indices (MCI), experimental parameters and random variables, eleven properties of organic solvents. Two model methodologies are used to test the different descriptors: the multilinear least-squares (MLS) methodology and the Artificial Neural Network (ANN) methodology. The top three quantitative structure–property relationships (QSPR) for each property are chosen with the MLS method. The indices of these three QSPRs were used to train the ANNs that selected the best training sets of indices to estimate the evaluation sets of…

Vertex (graph theory)Multilinear mapQuantitative structure–activity relationshipArtificial neural networkGeneral Chemical EngineeringGeneral ChemistryBiological systemRandom variableMathematicsRSC Adv.
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Exploiting ongoing EEG with multilinear partial least squares during free-listening to music

2016

During real-world experiences, determining the stimulus-relevant brain activity is excitingly attractive and is very challenging, particularly in electroencephalography. Here, spectrograms of ongoing electroencephalogram (EEG) of one participant constructed a third-order tensor with three factors of time, frequency and space; and the stimulus data consisting of acoustical features derived from the naturalistic and continuous music formulated a matrix with two factors of time and the number of features. Thus, the multilinear partial least squares (PLS) conforming to the canonical polyadic (CP) model was performed on the tensor and the matrix for decomposing the ongoing EEG. Consequently, we …

ta113Multilinear mapmedicine.diagnostic_testBrain activity and meditationSpeech recognition02 engineering and technologyElectroencephalographyta3112Matrix decomposition03 medical and health sciences0302 clinical medicinetensor decompositionFrequency domainPartial least squares regression0202 electrical engineering electronic engineering information engineeringmedicineSpectrogramOngoing EEG020201 artificial intelligence & image processingmusicTime domain030217 neurology & neurosurgerymultilinear partial least squaresMathematics
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