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1、ThispageintentionallyleftblankHilbertSpaceswithApplicationsLokenathDebnathandPiotrMikusinski´ThispageintentionallyleftblankHilbertSpaceswithApplicationsThirdEditionLokenathDebnathUniversityofTexasPanAmericanPiotrMikusinski´UniversityofCentralFloridaAMSTERDAM•BOSTON•HEIDELBERG•LONDON•NEWYORK•OXFO
2、RD•PARIS•SANDIEGO•SANFRANCISCO•SINGAPORE•SYDNEY•TOKYOElsevierAcademicPress30CorporateDrive,Suite400,Burlington,MA01803,USA525BStreet,Suite1900,SanDiego,California92101-4495,USA84TheobaldsRoad,LondonWC1X8RR,UKThisbookisprintedonacid-freepaper.∞Copyright©2005,ElsevierInc.Allrightsreserved.Noparto
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5、ginPublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibraryISBN13:978-0-12-2084386ISBN10:0-12-208438-1ForallinformationonallElsevierAcademicPresspublicationsvisitourWebsiteatwww.books.elsevier.comPrintedintheUnitedStatesofAmerica050607080910987654321Thisbookisdedicatedtothememo
6、ryofourfathers:JOGESHCHANDRADEBNATHandJANMIKUSINSKI´ThispageintentionallyleftblankContentsPrefacetotheThirdEditionxiPrefacetotheSecondEditionxiiiPrefacetotheFirstEditionxvCHAPTER1NormedVectorSpaces11.1Introduction11.2VectorSpaces21.3NormedSpaces81.4BanachSpaces191.5LinearMappings251.6Contraction
7、MappingsandtheBanachFixedPointTheorem321.7Exercises34CHAPTER2TheLebesgueIntegral392.1Introduction392.2StepFunctions402.3LebesgueIntegrableFunctions452.4TheAbsoluteValueofanIntegrableFunction482.5SeriesofIntegrableFunctions50
