linear systems and operators in hilbert space

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1、McGRAW-HILLINTERNATIONALBOOKCOMPANYNewYorkSt.LouisSanFranciscoAucklandBogotaGuatemalaHamburgJohannesburgLisbonLondonMadridMexicoMontrealNewDelhiPanamaParisSanJuanS$oPauloSingaporeSydneyTokyoTorontoPAULA.FUHRMANNDepartmentofMathematicsBenGurionUniversityoftheNegevBeerSheva,IsraelLinearSy

2、stemsandOperatorsinHilbertSpaceBritishLibraryCataloguingisPublicationDataFuhrmann,PaulA.LinearsystemsandoperatorsinHilbertspace.1.Hilbertspace2.LinearoperatorsI.Title515'.73QA322.47840976ISBN0-07-022589-3LINEARSYSTEMSANDOPERATORSINHILBERTSPACECopyright®1981byMcGraw-Hill,Inc.Allrightsres

3、erved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronical,mechanical,photocopying,recordingorotherwise,withoutthepriorwrittenpermissionofthepublisher.2345MOC8321CONTENTSChapterI.LinearalgebraandfinitedimensionalsystemsIntroduc

4、tion1.Ringsandmodules22.Polynomialmodules63.TheSmithcanonicalform124.Structureoflineartransformations155.Linearsystems286.Reachability,observability,andrealizations317.Hankelmatrices328.Simulationandisomorphism349.Transferfunctionsandtheirfactorizations3810.Realizationtheory3911.Polynom

5、ialsystemmatrices4312.Generalizedresultanttheorem4613.Feedback50Notesandreferences62ChapterII.OperatorsinHilbertspace63I.GeometryofHilbertspace632.BoundedoperatorsinHilbertspace703.Unboundedoperators774.Representationtheorems835.Thespectraltheorem936.Spectralrepresentations1047.TheDougl

6、asfactorizationtheoremandrelatedresults1248.Shifts,isometries,andtheWolddecomposition1269.Contractions,dilations,andmodels129viiviiiCONTENTS10.Semigroupsofoperators11.Theliftingtheorem12.ElementsofHZtheory13.Modelsforcontractionsandtheirspectra14.Thefunctionalcalculusforcontractions15.J

7、ordanmodelsNotesandreferencesChapterIII.LinearsystemsinHilbertspaceI.Fundamentalconcepts2.Hankeloperatorsandrealizationtheory3.Restrictedshiftsystems4.Spectralminimalityofrestrictedshiftsystems5.Degreetheoryforstrictlynoncyclicfunctions6.Continuoustimesystems7.SymmetricsystemsN