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M.Reed 、B.Simon 编 / 世界图书出版公司 / 2003-06 / 平装
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现代数学物理方法(第4卷)
WiththepublicationofVolumesIIIandIVwehavecompletedourpresentationofthematerialwhichweoriginallyplannedas"VolumeII"atthetimeofpublicationofVolumeI.WeoriginallypromisedthepublisherthattheentireserieswouldbecompletedninemonthsafterwesubmittedVolumeI.Well!Wehavelistedthecontentsoffuturevolumesbelow.Wearenotfoolhardyenoughtomakeanypredictions.
PrefaceIntroductionContentsofOtherVolumesXII:PERTURBATIONOFPOINTSPECTRA1.Finite-dimensionalperturbationtheoryAppendixAlgebraicandgeometricmultiplicityofeigenvaluesoffinitematrices2.Regularperturbationtheory3.Asymptoticperturbationtheory4.Summabilitymethodsinperturbationtheory5.Spectralconcentration6.ResonancesandtheFermigoldenruleNotesProblemsXlII:SPECTRALANALYSIS1.Therain-maxprinciple2.BoundstatesofSchr‘6dingeroperatorsI:Quantitativemethods3.BoundstatesofSchr‘odingeroperatorsII:QualitativetheoryA.Isdisc(H)finiteorinfinite?B.BoundsonN(V)inthecentralcaseC.BoundsonN(V)inthegeneraltwo-bodycase4.LocatingtheessentialspectrumI:Weyl'stheorem5.LocatingtheessentialspectrumIII:TireHVZtheorem6.TheabsenceofsingularcontinuousspectrumI:Generaltheory7.TheabsenceofsingularcontinuousspectrumII:SmoothperturbationsA.WeaklycoupledquantumsystemsB.PositivecommutatorsandrepulsivepotentialsC.Localsmoothnessandwaveoperatorsforrepulsivepotentials8.TheabsenceofsingularcontinuousspectrumIII:WeightedL2spaces9.Thespectrumofctensorproducts10.TheabsenceofsingularcontinuousspectrumIV:Dilationanalyticpotentials11.Propertiesofeigenfitnctions12.NondegeneracyofthegroundstateAppendix1TheBeurling-DenycriteriaAppendix2TheLevy-Khintchinecformula13.AbsenceofpositiveeigenvaluesAppendixUniquecontinuationtheoremsforSchrodingeroperators14.Compactnesscriteriaandoperatorswithcompactresolvent15.Theasymptoticdistributionofeigenvalues16.Schr6dingeroperatorswithperiodicpotentials17.Anintroductiontothespecraltheoryofnon-self-adjointoperatorsNotesProblemsListofSymbolsIndex
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