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1、SpectralTheoryofBlockOperatorMatricesandApplicationsThispageintentionallyleftblankSpectralTheoryofBlockOperatorMatricesandApplicationsChristianeTretterUniversitatBern,SwitzerlandImperialCollegePressICPPublishedbyImperialCollegePress57SheltonStreetCoventGardenLondonWC
2、2H9HEDistributedbyWorldScientificPublishingCo.Pte.Ltd.5TohTuckLink,Singapore596224USAoffice:27WarrenStreet,Suite401-402,Hackensack,NJ07601UKoffice:57SheltonStreet,CoventGarden,LondonWC2H9HEBritishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisbookisavail
3、ablefromtheBritishLibrary.SPECTRALTHEORYOFBLOCKOPERATORMATRICESANDAPPLICATIONSCopyright©2008byImperialCollegePressAllrightsreserved.Thisbook,orpartsthereof,maynotbereproducedinanyformorbyanymeans,electronicormechanical,includingphotocopying,recordingoranyinformations
4、torageandretrievalsystemnowknownortobeinvented,withoutwrittenpermissionfromthePublisher.Forphotocopyingofmaterialinthisvolume,pleasepayacopyingfeethroughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,USA.Inthiscasepermissiontophotocopyisnotrequired
5、fromthepublisher.ISBN-13978-1-86094-768-1ISBN-101-86094-768-9PrintedinSingapore.ZhangJi-SpectralTheoryofBlock.pmd19/3/2008,4:55PM3rdSeptember200811:35WSPC/BookTrimSizefor9inx6inmybook9x6PrefaceBlockoperatormatricesarematricestheentriesofwhicharelinearoper-atorsbetwee
6、nBanachorHilbertspaces.Theyariseinvariousareasofmathematicsanditsapplications:insystemstheoryasHamiltonians(see[CZ95]),inthediscretizationofpartialdi erentialequationsaslargeparti-tionedmatricesduetosparsitypatterns(see[SAD+00]),insaddlepointproblemsinnon-linearanaly
7、sis(see[BGL05]),inevolutionproblemsaslinearizationsofsecondorderCauchyproblems(see[EN00]),andaslin-earoperatorsdescribingcoupledsystemsofpartialdi erentialequations.Suchsystemsoccurwidelyinmathematicalphysics,e.g.in
uidmechanics(see[Cha61]),magnetohydrodynamics(see[L
8、if89]),andquantummechan-ics(see[Tha92]).Inalltheseapplications,thespectralpropertiesofthecorrespondingblockoperatormatricesareofvit
