2013
Multiscale data sampling and function extension
Bermanis A, Averbuch A, Coifman R. Multiscale data sampling and function extension. Applied And Computational Harmonic Analysis 2013, 34: 15-29. DOI: 10.1016/j.acha.2012.03.002.Peer-Reviewed Original ResearchSequence of approximationsGaussian kernel matrixData pointsAdaptive gridSpecial decompositionMultiscale schemeKernel matrixMultiscale decompositionGaussian kernelInterpolation methodMutual distanceData samplingFine hierarchyExtension methodEmpirical functionHierarchical procedureFunction extensionApproximationExtensionDecompositionPointKernelSchemeSubsamplingGrid
2006
Geometric harmonics: A novel tool for multiscale out-of-sample extension of empirical functions
Coifman R, Lafon S. Geometric harmonics: A novel tool for multiscale out-of-sample extension of empirical functions. Applied And Computational Harmonic Analysis 2006, 21: 31-52. DOI: 10.1016/j.acha.2005.07.005.Peer-Reviewed Original ResearchEntire space RnProlate spheroidal wave functionsLaplace-Beltrami operatorSpheroidal wave functionsFunction fSubmanifold of RnNyström methodSpace RnFourier modesSample extensionGeometric harmonicsEmpirical functionWave functionsSimple schemeExtension schemeLarge domainsSpecific familySchemeRnIntrinsic frequency spectrumExtensionFrequency spectrumSubmanifoldsEigenfunctionsSlepian
1994
Selection of best bases for classification and regression
Coifman R, Saito N. Selection of best bases for classification and regression. 1994, 51. DOI: 10.1109/wits.1994.513882.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