简介：Inthispaper,theauthoratfirstdevelopsamethodtostudyconvergenceofthecascadealgorithminaBanachspacewithoutstableassumptionontheinitial(seeTheorem2.1),andthenappliesthepreviousresultontheconvergencetocharacterizingcompactlysupportedrefinabledistributionsinfractionalSobolevspacesandHoldercontinuousspaces(seeTheorems3.1,3.3,and3.4).Finallytheauthorappliestheabovecharacterizationtochoosingappropriateinitialtoguaranteetheconvergenceofthecascadealgorithm(seeTheorem4.2).
简介：LetMbead×dexpansivematrix,andFL2(Ω)beareducingsubspaceofL2(Rd).ThispapercharacterizesboundedmeasurablesetsinRdwhicharethesupportsofFouriertransformsofM-refinableframefunctions.Asapplications,wederivethecharacterizationofboundedmeasurablesetsasthesupportsofFouriertransformsofFMRA(W-typeFMRA)framescalingfunctionsandMRA(W-typeMRA)scalingfunctionsforFL2(Ω),respectively.Someexamplesarealsoprovided.
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