简介：LetB(H)bethealgebraofalltheboundedlinearoperatorsonaHilbertspaceH.ForA,PandQinB(H),ifthereexistsanoperatorX∈B(H)suchthatAPXQA=A,XQAPX=X,(QAPX)*=QAPXand(XQAP)*=XQAP,thenXissaidtobetheΓ-inverseofAassociatedwithPandQ,anddenotedbyAP,Q+.Inthisnote,wepresentsomenecessaryandsu?cientconditionsforwhichA+P,Qexists,andgiveanexplicitrepresentationofAP,Q+(ifAP,Q+exists).

简介：Wecharacterizepolynomialgrowthofcosinefunctionsintermsoftheresolventofitsgeneratorandgiveanecessaryandsufficientconditionforacosinefunctionwithaninfinitesimalgeneratorwhichispolynomiallybounded.

简介：Letp(z)=akzkbesuchthat|p(eip)|≤1forRand|p(1)|=a[0,1].AninequalityofDewanandCavilforthesum|av|+|au|,0≤u

简介：Kytmanov和Myslivets给了单个积分的特殊Cauchy主要价值在上与光滑的边界围住严格地假的凸的领域。借助于这Cauchy不可分的主要价值，相应单个积分和一个作文公式被获得。这个作文公式与平常的处于良好的竟技状态相当不同。作为一个应用程序，相应单个不可分的方程和单个不可分的方程的系统也被讨论。

简介：Theboundedparameterestimationproblemanditssolutionleadtomoiemeaningfulresults.Itssuperiorperformanceisduetothefactthatthenewmethodguaranteesthattheeffectoftheuncertaintieswillneverbeunnecessarilyoverestimated.Wethenconsiderhowtoupdateanddowndatetheboundedparameterestimationproblem.WhenupdatinganddowndatingofSVDareusedtothenewproblem,specialtechnologiesaretakentoavoidformingUandVexplicitly,thenincreasethealgorithmperformance.BecauseofthelinkbetweentheboundedparameterestimationandTikhonovregularizationprocedure,wepointoutthatouralgorithmscanalsobeusedtomodifyregularizationproblem.

简介：TheestimationsoftheboundsoftheBlochconstantoflocallybiholomorphicmappingsonirreducibleboundedsymmetricdomainsaregiven.Whenthedomainisaunitcircle,theestimationofthelowerboundsisjustthefamousone-halfestimation.

简介：对每真实值的凸的功能在一个集合上上面围住的保证连续，集合应该怎么“厚”吗？为在Banach空间E的对称的集合A，这篇论文的答案是：如果并且仅当下列二个条件成立，在A上上面围住的每真实值的凸的功能在E上是连续的：我)跨度A有有限co-dimentions和ii)coA有非空的相对内部。这篇论文也证明子集A在E被包含令人满意如果，在A上上面围住的每真实值的凸的功能在E上是连续的(并且仅当)每真实值线性功能在A上上面跳了在E上是连续的，它也等价于那在A上围住的每真实值的凸的功能在E上是连续的。

简介：ThispaperpresentsanewfamilyofsolutionstothesingularlyperturbedAllen-Cahnequationα~2Δu+u(1-u~2)=0inasmoothboundeddomainΩR~3,withNeumannboundaryconditionandα>0asmallparameter.Thesesolutionshavethepropertythatasα→0,theirlevelsetscollapseontoaboundedportionofacompleteembeddedminimalsurfacewithfinitetotalcurvatureintersecting?Ωorthogonallyandthatisnon-degeneraterespectto?Ω.Theauthorsprovideexplicitexamplesofsurfacestowhichtheresultapplies.

简介：Inthispaper,thenotionoftheboundedcompactapproximationproperty(BCAP)ofapair[Banachspaceanditssubspace]isusedtoprovethatifXisaclosedsubspaceofL∞withtheBCAP,thenL∞/XhastheBCAP.WealsoshowthatX*hastheλ-BCAPwithconjugateoperatorsifandonlyifthepair(X,Y)hastheλ-BCAPforeachfinitecodimensionalsubspaceY∈X.LetMbeaclosedsubspaceofXsuchthatM⊥iscomplementedinX*.IfXhasthe(bounded)approximationpropertyoforderp,thenMhasthe(bounded)approximationpropertyoforderp.

简介：LetDbeaboundedC3-domaininRdand(aij)beaboundedsymmetricmatrixdefinedonD.Considerthesymmetricform（u,v）=1/2∫Daij（x）（u（x））/（xi）（v（x））/（xj）dx,u,v∈H1（D）.UndersomeassumptionsitisshownthatthediffusionprocessassociatedwiththeregularDirichletspace(,（H1（D））onL2（D）canbecharacterizedasauniquesolutionofacertainstochasticdifferentialequation.

简介：InthisarticlewestudyholomorphicisometriesofthePoincar'ediskintoboundedsymmetricdomains.EarlierwesolvedtheproblemofanalyticcontinuationofgermsofholomorphicmapsbetweenboundeddomainswhichareisometriesuptonormalizingconstantswithrespecttotheBergmanmetric,showinginparticularthatthegraphV0ofanygermofholomorphicisometryofthePoincar'ediskΔintoanirreducibleboundedsymmetricdomainΩ€CNinitsHarish-Chandrarealizationmustextendtoanaffine-algebraicsubvarietyVC×CN=CN+1,andthattheirreduciblecomponentofV∩(Δ×Ω)containingV0isthegraphofaproperholomorphicisometricembeddingF:Δ→Ω.Inthisarticlewestudyholomorphicisometricembeddingswhichareasymptoticallygeodesicatageneralboundarypointb∈Δ.Startingwiththestructuralequationforholomor-phicisometriesarisingfromtheGaussequation,weobtainbycovariantdifferentiationanidentityrelatingcertainholomorphicbisectionalcurvaturestotheboundarybehaviorofthesecondfundamentalformσoftheholomorphicisometricembedding.Usingthenonpositivityofholomorphicbisectionalcurvaturesonaboundedsymmetricdomain,weprovethatσmustvanishatageneralboundarypointeithertotheorder1ortotheorder21,calledaholomorphicisometryofthefirstresp.secondkind.Wedealwithspecialcasesofnon-standardholomorphicisometricembeddingsofsuchmaps,showingthattheymustbeasymptoticallytotallygeodesicatageneralboundarypointandinfactofthefirstkindwheneverthetargetdomainisaCartesianproductofcomplexunitballs.WealsostudytheboundarybehaviorofanexampleofholomorphicisometricembeddingfromthePoincar'ediskintoaSiegelupperhalf-planebyanexplicitdeterminationoftheboundarybehaviorofholomorphicsectionalcurvaturesinthedirectionstangenttotheembeddedPoincar'edisk,showingthatthemapisindeedasymptoticallytotallygeodesicatageneralboundarypointandofthefirstkind.Fo

简介：为>1，让d在bidisk和一项复杂措施上表示加权的Lebesgue措施令人满意一些Carleson类型条件。在这份报纸，我们为Toeplitz操作员$T_显示出一个足够、必要的条件{\bar\mu}在加权的Bergman空间L上要跳或压缩的^\alpha$一1(d)。

简介：TheauthorscharacterizetheorderboundednessofweightedcompositionoperatorsactingbetweenDirichlettypespaces.

简介：RecentlyGuointroducedintegratedMeyer-KonigandZelleroperatorsandstudiedtherateofconvergenceforfunctionofboundedvariation.Inthisnotewegiveasharpestimatefortheseoperators.

简介：

简介：WeknowthattheBoxdimensionoff(x)∈C~1[0,1]is1.Inthispaper,weprovethattheBoxdimensionofcontinuousfunctionswithboundedvariationisstill1.Furthermore,BoxdimensionofWeylfractionalintegralofabovefunctionisalso1.

简介：Thispapergivesthedegreeofapproximationoffunctionofboundedvariationbythepartialsumsofcon-jngateLegendre-FourierSeries.

简介：Inthispaperweshowthatinerrorestimates,theconditionnumberκ(T)ofanyinvertiblelinearboundedoperatorTinBanachspacesisminimal.WealsoextendtheHahn-Banachtheoremandotherrelatedresults.

简介：WegiveaSchwarz-PickestimateforboundedholomorphicfunctionsonunitballinC~n,andgeneralizesomeearlyworkofSchwarz-PickestimatesforboundedholomorphicfunctionsonunitdiskinC.

简介：Theexistenceofboundedandunboundedsolutionstononlinearreaction-diffusionproblemut=△Φ(u)+F(u,x,t)withinitinalorinitial-boundaryconditionsisdiscussedwhenu=u(x,t),x∈R，Simplecriteriaaregiven.