2017
Reconstruction of normal forms by learning informed observation geometries from data
Yair O, Talmon R, Coifman RR, Kevrekidis IG. Reconstruction of normal forms by learning informed observation geometries from data. Proceedings Of The National Academy Of Sciences Of The United States Of America 2017, 114: e7865-e7874. PMID: 28831006, PMCID: PMC5617245, DOI: 10.1073/pnas.1620045114.Peer-Reviewed Original ResearchNormal formNonlinear differential equationsDynamical systems theoryAppropriate normal formFundamental physical quantitiesDifferential equationsDynamical regimesState variablesPhysical quantitiesPhysical lawsSystems theoryGeometry learningEmpirical observationsObservation geometryHeart of scienceDynamicsPrior knowledgeEquationsRealizationLawParametersGeometryTheoryExplicit referenceForm
2006
Diffusion maps
Coifman R, Lafon S. Diffusion maps. Applied And Computational Harmonic Analysis 2006, 21: 5-30. DOI: 10.1016/j.acha.2006.04.006.Peer-Reviewed Original ResearchMarkov matrixSpectral graph theoryDiffusion mapsGraph theoryMultiscale geometryGeometric descriptionGeometric counterpartMarkov processComplex geometric structuresData parametrizationGeometric structureEfficient representationDiffusion processDimensionality reductionSpectral propertiesData setsEigenfunctionsMachine learningMatrixParametrizationCoordinatesGeometryTheoryVariety of contextsFramework
1991
Fast wavelet transforms and numerical algorithms I
Beylkin G, Coifman R, Rokhlin V. Fast wavelet transforms and numerical algorithms I. Communications On Pure And Applied Mathematics 1991, 44: 141-183. DOI: 10.1002/cpa.3160440202.Peer-Reviewed Original ResearchPseudo-differential operatorsClass of algorithmsLinear operatorsTheory of waveletsN matrixNumerical experimentsArbitrary vectorOrder ONumerical applicationsNarrow classAlgorithm IOperatorsDetailed analytical informationIntractable problemClassAlgorithmMatrixAnalytical informationVectorTheorySchemeO operationsProblemWavelets
1990
Multiresolution Analysis in Non-Homogeneous Media
Coifman R. Multiresolution Analysis in Non-Homogeneous Media. Inverse Problems And Theoretical Imaging 1990, 259-262. DOI: 10.1007/978-3-642-75988-8_25.Peer-Reviewed Original Research
1989
Multiresolution Analysis in Non-Homogeneous Media
Coifman R. Multiresolution Analysis in Non-Homogeneous Media. Inverse Problems And Theoretical Imaging 1989, 259-262. DOI: 10.1007/978-3-642-97177-8_25.Peer-Reviewed Original Research
1985
Some new function spaces and their applications to Harmonic analysis
Coifman R, Meyer Y, Stein E. Some new function spaces and their applications to Harmonic analysis. Journal Of Functional Analysis 1985, 62: 304-335. DOI: 10.1016/0022-1236(85)90007-2.Peer-Reviewed Original ResearchTent spacesHarmonic analysisHardy spacesFamily of spacesNew function spaceLipschitz curvesFunction spacesAtomic decompositionCauchy integralCarleson inequalitySquare functionMaximal functionSpaceTheoryBasic techniquesInequalitySimplificationIntegralsCorollaryMultilinear analysisApplicationsFunctionExtensionUnification
1982
A theory of complex interpolation for families of Banach spaces
Coifman R, Cwikel M, Rochberg R, Sagher Y, Weiss G. A theory of complex interpolation for families of Banach spaces. Advances In Mathematics 1982, 43: 203-229. DOI: 10.1016/0001-8708(82)90034-2.Peer-Reviewed Original Research