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1、LectureNotesinMathematicsAcollectionofinformalreportsandseminarsEditedbyA.Dold,HeidelbergandB.Eckmann,Z(Jrich261AlainGuichardetFacult6desSciencesdePoitiers,FranceSymmetricHilbertSpacesandRelatedTopicsInfinitelyDivisiblePositiveDefiniteFunctionsContinuousProductsandTensorProductsGau
2、ssianandPoissonianStochasticProcessesSpringer-VerlagBerlin.HeidelbergNewYork1972AMSSubjectClassifications(1970):46C10,46M05,60G15,81A20ISBN3-540-05803-6Springer-VerlagBerlinHeidelberg-NewYorkISBN0-387-05803-6Springer-VertagNewYorkHeidelberg-BerlinThisworkissubjecttocopyright.Allrig
3、htsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallythoseoftranslation,reprinting,re-useofillustrations,broadcasting,reproductionbyphotocopyingmachineorsimilarmeans,andstorageindatabanks.Under§54oftheGermanCopyrightLawwherecopiesaremadeforotherthanprivateuse,af
4、eeispayabletothepublisher,theamountofthefeetobedeterminedbyagreementwiththepublisher.©bySpringer-VerlagBerlin-Heidelberg1972.LibraryofCongressCatalogCardNumber72-76390.PrintedinGermany.Offsetdruck:JuliusBeltz,Hemsbach/Bergstr.TableofContentIntroduction..........................Chap
5、terI.Thesymmetricmeasurespaceofameasurespace...31.1.Thesymmetricsetofaset...........31.2.ThefunctorSonthecategoryofsets......41.3.ThesymmetricBorelspaceofaBorelspace.61.4.Thesymmetricmeasurespaceofameasurespace.71.5.Applicationtolinearprocessesandfactoredprobabilityspaces..........
6、.....12Chapter2.ThesymmetricHilbertspaceofaHilbertspace....182.1.Definitionsandgeneralproperties....~.182.2.TheunitaryoperatorsUA,b,candthegrouP~H.222.3.Relationwithsymmetricmeasurespaces.....28Chapter3.Positivedefinitefunctionsoftype(S).......303.1.Positivedefinitefunctions.......
7、....303.2.Positivedefinitefunctionsoftype(S).Definitionsandfirstproperties........353.3.Thecaseofcommutativelocallycompactgroups.38Chapter4.Conditionallypositivedefinitefunctionsandinfi-nitelydivisiblepositivedefinitefunctions.....474.1.Conditionallypositivedefinitematricesandkerne
8、ls...................474.2
