hong d., wang j., gardner r. real analysis with an introduction to wavelets (book draft, ap, 2005)(342s)_mcf_

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1、RealAnalysiswithanIntroductiontoWaveletsDonHongJianzhongWangRobertGardnerAuthoraddress:(D.Hong,R.Gardner)DepartmentofMathematicalandStatisticalSciences,EastTennesseeStateUniversity,John-sonCity,Tennessee(J.Wang)DepartmentofMathematicsandStatistics,SamHoustonStateUniversity,Huntsvill

2、e,TexasE-mailaddress,D.Hong:hong@etsu.eduE-mailaddress,J.Wang:mthjxw@shsu.eduE-mailaddress,R.Gardner:gardnerr@etsu.edu.Toourwives:Ying,Hui-Lan,andKathryn.Contents1.PrefacevChapter1.Fundamentals11.ElementarySetTheory12.RelationsandOrderings53.CardinalityandCountability124.TheTopology

3、ofRn18Chapter2.MeasureTheory311.ClassesofSets322.MeasuresonaRing363.OuterMeasuresandLebesgueMeasure424.MeasurableFunctions505.ConvergenceofMeasurableFunctions56Chapter3.TheLebesgueIntegral591.TheRiemannIntegralandtheLebesgueIntegral592.TheGeneralLebesgueIntegral653.ConvergenceandApp

4、roximationofLebesgueIntegrals704.LebesgueIntegralsinthePlane76Chapter4.SpecialTopicsofLebesgueIntegralandApplications811.DifferentiationandIntegration812.MathematicalModelsforProbability933.ConvergenceandLimitTheorems99Chapter5.VectorSpaces,HilbertSpaces,andtheL2Space1051.Groups,Fiel

5、ds,andVectorSpaces1052.InnerProductSpaces1143.TheSpaceL21204.ProjectionsandHilbertSpaceIsomorphisms1245.BanachSpaces132Chapter6.FourierAnalysis1411.FourierSeries142iiiivCONTENTS2.Parseval’sFormula1523.TheFourierTransformofIntegrableFunctions1604.FourierTransformsofSquareIntegrableFu

6、nctions1725.ThePoissonSummationFormula179Chapter7.OrthonormalWaveletBases1891.HaarWaveletBasis1912.MultiresolutionAnalysis1983.OrthonormalWaveletsFromMRA2054.OrthonormalSplineWavelets2155.FastWaveletTransforms2256.BiorthogonalWaveletBases236Chapter8.CompactlySupportedWavelets2451.Sy

7、mbolsofOrthonormalScalingFunctions2452.TheDaubechiesScalingFunctions2583.ComputationofDaubechiesScalingFunctions2664.WaveletPackets2755.CompactlySupportedBiorthogonalWaveletBases281Chapter9.WaveletsinSignalProcessing2891.Signals2892.Filters2973.CodingSignalsbyWaveletTransform3084.Fi

8、lterBanks316Appendi