简介:定义了向量筐函数的C-Stieltjes近似可表示算子,并研究了它的性质。另外,我们定义了向量值函数的近似C-Stieltjes积分,并证明了它的收敛定理。
简介:LetT=(T(t))t≥0beaboundedC-regularizedsemigroupgeneratedbyAonaBanachspaceXandR(C)bedenseinX.WeshowthatifthereisadensesubspaceYofXsuchthatforeveryx∈Y,σu(A,Cx),thesetofallpointsλ∈iRtowhich(λ-A)^-1Cxcannotbeextendedholomorphically,isatmostcountableandσr(A)NiR=Ф,thenTisstable.AstabilityresultforthecaseofR(C)beingnon-denseisalsogiven.Ourresultsgeneralizetheworkonthestabilityofstronglycontinuoussenfigroups.
简介:Inthispaper,weintroduceaconditionweakerthantheLpdifferentiability,whichwecallCpcondition.Weprovethatifafunctionsatisfiesthisconditionatapoint,thenthereexiststhebestlocalapproximationatthatpoint.WealsogiveanecessaryandsufficientconditionforthatafunctionbeLpdifferentiable.Inaddition,westudytheconvexityofthesetofclusterpointsofthenetofbestappoximationsoff,{Pe(f)}ase→0.
简介:LetGbeasecondcountablelocallycompactgroupoidwithHaarsystem{λuH},HbeaclosedsubgroupoidcontainingG^0withHaarsystem{λuH}.T.MasudaintroducedtheC^*-Groupoiddynamicsystem(G,A,α)anditsreducedcrossedproductCrea(G,A)in[2]:whereAisC^*-algebraαisthekomomorphismG→Aut(A).InthispapertheauthorintroducestheC^*-groupoiddynamicsystems(H,A,α/H)and(H\G2,A,^-α)inducedby(G,A,α)andprovesthatC*red(H,A)andC^*red(H\G^2,A)arestronglyMoritaequivalentMoreovertheinducedrepresentationfromC^*red(H,A)toC^*red(G,A)isgot.
简介:Risler&Trotmanin1997provedthatthemultiplicityofananalyticfunctiongermisleft-rightlipschitzinvariant,whichprovidedapartialanswertoZariskiconjecture.Inthisnote,basedontherecentworkofComte,Milman&Trotman,wegeneralizetheworkofthemtoprovethatthemultiplicityofaC~∞-differentiablefunctiongermisalsoleft-rightlipschitzinvariant.
简介:ThispapershowsthattheC1-curvedfiniteelementdevelopedbyBernadoningeneralcannotsatisfytheessentialboundaryconditionsonapproximateboundary.Furthermore,amodifiedC1-curvedfiniteelementisgiven,whichiscompatiblewiththeelementofArgyristriangleandcansatisfythehomogeneousDirichletboundaryconditionsonapproximateboundary.