简介:TheauthorsdefinethedirectionalhyperHilberttransformandgiveitsmixednormestimate.Thesimilarconclusionsforthedirectionalfractionalintegralofonedimensionarealsoobtainedinthispaper.Asanapplicationoftheaboveresults,theauthorsgivetheLp-boundednessforaclassofthehypersingularintegralsandthefractionalintegralswithvariablekernel.Moreover,asanotherapplicationoftheaboveresults,theauthorsprovethedimensionfreeestimateforthehyperRiesztransform.ThisisanextensionoftherelatedresultobtainedbyStein.
简介:LetS∞denotetheunitsphereinsomeinfinitedimensionalcomplexHilbertspace(H,<·,·>)Letz1,z2,…,z1bedistinctpointsonS∞Thispaperdealswithinterpolationofarbitrarydataonthezjbyafunctioninthelinearspanofthelfunctionswhenisasuitablefunctionthatoperatesonnonnegativedefinitematrices.Conditionsforthestrictpositivedefinitenessofthekernelareobtained.
简介:In[1-5],itwasinvestigaedtherealizationsofweightingpatternsinHilbertspaces.Thisnotedealswithdiscretesystemswhichhaveoperatorweightingpartterns.Theorems2-4arenecessaryandsufficientconditionsforJ-unitaryrealizationandforJ-selfadjoint
简介:获得了HilbertC^*-模之间的两个同构定理.作为推论,证明了C^*-代数上每个可数生成的HilbertC^*-模均稳定酉等价于A。
简介:Inthispaper,twoalgorithmsarepresentedforgeneratingtwocodescanlistsofanN-dimensionalHilbertcell,andaformalproofofthebackwardencodingalgorithmisgiven.Onthebasisoftheself-simi-laritypropertiesofaHilbertcurve,thispapergivesanovelalgorithmforgeneratingastaticevolvementruletablethroughanalyzingaHilbertcell.Bylookingupthestaticevolvementruletable,theN-dimensionalHilbertmappingsareefficientlyimplemented.
简介:Considerthepositived-dimensionallatticed+(d≥2)withpartialordering≤,let{XK;K∈d+}bei.i.d.randomvari-ablestakingvaluesinarealseparableHilbertspace(H,||·||)withmeanzeroandcovarianceoperator∑,andsetpartialsumsSN=∑K≤NXK,K,N∈d+.Undersomemomentconditions,weobtainthepreciseasymptoticsofakindofweightedinfiniteseriesforpartialsumsSNasε0byusingthetruncationandapproximationmethods.TheresultsarerelatedtotheconvergenceratesofthelawofthelogarithminHilbertspace,andtheyalsoextendtheresultsof(GutandSpǎtaru,2003).
简介:本文给出了Hibert空间中正交基扰动的一个结果及一个实例。
简介:Westudythenormretrievalbyprojectionsonaninfinite-dimensionalHilbertspaceH.Let{e_i}_(i∈I)beanorthonormalbasisinHandW_i={e_i}~⊥foralli∈I.Weshowthat{W_i}_(i∈I)doesnormretrievalifandonlyifIisaninfinitesubsetofN.Wealsogivesomepropertiesofnormretrievalbyprojections.
简介:ThemainobjectiveofthisworkistodecomposeorthogonallythereproducingkernelsHilbertspaceusinganyconditionallypositivedefinitekernelsintosmalleronesbyintroducingthetheoryofpowerkernels,andtoshowhowtodothisdecompositionrecursively.Itmaybeusedtosplitlargeinterpolationproblemsintosmalleroneswithdifferentkernelswhicharerelatedtotheoriginalkernels.Toreachthisobjective,wewillreconstructthereproducingkernelsHilbertspaceforthenormalizedandtheextendedkernelsandgivetherecursivealgorithmofthisdecomposition.
简介:Inthispaper,wefirstdeterminetherelationsamongthebestboundsAandBoftheg-frame,theg-frameoperatorSandthepre-frameoperatorQandgiveanecessaryandsufficientconditionforag-framewithboundsAandBinacomplexHilbertspace.Wealsointroducethedefinitionofag-framesequenceandobtainanecessaryandsufficientconditionforag-framesequencewithboundsAandBinacomplexHilbertspace.Lastly,weconsiderthestabilityofag-framesequenceforacomplexHilbertspaceunderperturbation.
简介:在N-解析函数类中,对于无穷直线上的Riemann-Hilbert边值问题,通过轴的对称扩张法将其转化为在附加条件下相应的Riemann边值问题,从而建立了其齐次和非齐次问题的可解性理论。
简介:LetR0,nbetherealCliffordalgebrageneratedbye1,e2,···,ensatisfyingeiej+ejei=-2δij,i,j=1,2,···,n.e0istheunitelement.Letbeanopenset.AfunctionfiscalledleftgeneralizedanalyticiniffsatisfiestheequationLf=0,(0.1)whereL=q0e0θx0+q1e1θx1+···+qnenθxn,qi>0,i=0,1,···,n.Inthisarticle,wefirstgivethekernelfunctionforthegeneralizedanalyticfunction.Further,theHilbertboundaryvalueproblemforgeneralizedanalyticfunctionsinRn+1+willbeinvestigated.