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1、LectureNotesinMathematics1577Editors:A.Dold,HeidelbergB.Eckmann,ZtirichF.Takens,GroningenNobuakiObataWhiteNoiseCalculusandFockSpaceSpringer-VerlagBerlinHeidelbergNewYorkLondonParisTokyoHongKongBarcelonaBudapestAuthorNobuakiObataDepartmentofMathematicsSchoolofScienceNagoyaUniversit
2、yNagoya,464-01,JapanMathematicsSubjectClassification(1991):46F25,46E50,47A70,47B38,47D30,47D40,60H99,60J65ISBN3-540-57985-0Springer-VerlagBerlinHeidelbergNewYorkISBN0-387-57985-0Springer-VerlagNewYorkBerlinHeidelbergCIP-DataappliedforThisworkissubjecttocopyright.Allrightsarereserv
3、ed,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,re-useofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherway,andstorageindatabanks.Duplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoft
4、heGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer-Verlag.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.9Springer-VerlagBerlinHeidelberg1994PrintedinGermanySPIN:1013001946/3140-543210-Printedonacid-freepaper
5、ContentsIntroductionviiIPrerequisites11.1Locallyconvexspaces!ngeneral......................11.2CountablyHilbert~paces..........................31.3Nuclear,'pacesandkerneltheorem....................71.4StandardCH-spacescffunctions......................111.5Bochner-Minlostheorem....
6、......................161.6Furtlcernotationalremarks.........................17Bibliographical~otes............................182WhiteNoiseSpace192.1Gaussianmeasure..............................192.2Wick-orderedpolynomials.........................232.3Wiener-ItS-Segalisomorphisma
7、ndFockspace..............28Bibliographicalnotes............................323WhiteNoiseFunctionals333.1StandardConstruction...........................333.2Continuousversiontheorem........................383.3S-transform.................................483.4Contractionoftensorprod
8、ucts.......................533.5W
