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1、LINEAROPERATOREQUATIONSApproxirnationandRegularizationThispageintentionallyleftblankLINEAROPEATOREQUATIONSApproximationandregularizationM.THAMBANNAIRIndianInstituteofTechnologyMadrasIndiaWorldScientificNEWJERSEY.LONDON.SINGAPORE.BEIJING.SHANGHAI.HONGKONG.TAIPEI.CHENNAIThispage
2、intentionallyleftblankPublishedbyWorldScientificPublishingCo.Pte.Ltd.5TohTuckLink,Singapore596224USAoffice:27WarrenStreet,Suite401-402,Hackensack,NJ07601UKoffice:57SheltonStreet,CoventGarden,LondonWC2H9HELibraryofCongressCataloging-in-PublicationDataNair,M.Thamban.Linearoperat
3、orequations:approximationandregularization/byM.ThambanNair.p.cm.Includesbibliographicalreferencesandindex.ISBN-13:978-981-283-564-2(hardcover:alk.paper)ISBN-10:981-283-564-4(hardcover:alk.paper)1.Linearoperators.2.Operatorequations.I.Title.QA329.2.N352009515'.7246--dc222009007
4、531BritishLibraryCataloguing-in-PublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary.Copyright©2009byWorldScientificPublishingCo.Pte.Ltd.Allrightsreserved.Thisbook,orpartsthereof,maynotbereproducedinanyformorbyanymeans,electronicormechanical,includingphot
5、ocopying,recordingoranyinformationstorageandretrievalsystemnowknownortobeinvented,withoutwrittenpermissionfromthePublisher.Forphotocopyingofmaterialinthisvolume,pleasepayacopyingfeethroughtheCopyrightClearanceCenter,Inc.,222RosewoodDrive,Danvers,MA01923,USA.Inthiscasepermissio
6、ntophotocopyisnotrequiredfromthepublisher.PrintedinSingapore.EH-LinearOperatorEquations.pmd13/20/2009,6:32PMMarch20,200912:10WorldScientificBook-9inx6inws-linopbkDedicatedtoMyMotherMelothParvathiAmmavMarch20,200912:10WorldScientificBook-9inx6inws-linopbkThispageintentionallyleft
7、blankMarch20,200912:10WorldScientificBook-9inx6inws-linopbkPrefaceManyproblemsinscienceandengineeringhavetheirmathematicalformu-lationasanoperatorequationTx=y,whereTisalinearornonlinearoperatorbetweencertainfunctionspaces.Inpractice,suchequationsaresolvedapproximatelyusingnumer
8、icalmethods,astheirexactsolutionmaynotbeoftenpossibleormaynot
