简介:SupposethatCisthecomplexplaneandkisanon-negativeinteger.DefinefunctionsNk-(x)=|x|kifkisevenandNk(x)=x|x|k-1ifkisodd.SomeapproximationpropertiesofNk-(x)’sisdiscussedandanewexampleofaTchebycheffsystemisgivenout.
简介:深化对本性谱的认识;给出∑_e~n(n≥2)型Banach空间上的摄动类问题的反面回答.
简介:Inthispaper,weshowthatapositiverecurrentuidqueueisautomaticallyV-uniformlyergodicforsomefunctionV≥1butneveruniformlyergodic.Thisrevealsasimilarityofergodicitybetweenafluidqueueandaquasi-birth-and-deathprocess.AsabyproductofV-uniformergodicity,wederivecomputableboundsontheexponentialmomentsofthebusyperiod.
简介:Thestudyofoperatorssatisfyingσja(T)=σa(T)isofsignificantinterest.Doesσja(T)=σa(T)forn-perinormaloperatorT∈B(H)ffThisquestionwasraisedbyMecheriandBraha[Oper.Matrices6(2012),725–734].Inthenoteweconstructacounterexampletothisquestionandobtainthefollowingresult:ifTisan-perinormaloperatorinB(H),thenσja(T)\{0}=σa(T)\{0}.Wealsoconsidertensorproductofn-perinormaloperators.
简介:Letr,1p={f:fr-1isabs.cont.onI=[a,b],fisperiodiewithperiodH(=b-a),f(x1)=0,‖f(r)‖p≤0},wherex1isanyfixedpointin[a,b].TheauthorfindstheKolmogorov,Gel’land,linear,andBerusteinn-widthsofr,1pinLp(I)fornodd,∞>p>1.Theoptimalsubspacesandoperatorsarealsofound.
简介:ThepresentpaperdealswithfindingofconstantoccurringintheorderofapproximationofthefunctionofLipα(O<α<1)classbyusing(N,p)operator.Obviouslythefactor1/(1-α)becomeslargewhenαiscloseto1.Wehaveshowntheroleofthisfactorintheconstantofapproximation.
简介:Itisknownfromclassicaldifferentialgeometrythatonecanreconstructacurvewith(n-1)prescribedcurvaturefunctions,ifthesefunctionscanbedifferentiatedacertainnumberoftimesintheusualsenseandifthefirst(n-2)functionsarestrictlypositive.ItisestablishedherethatthisresultstillholdsundertheassumptionthatthecurvaturefunctionsbelongtosomeSobolevspaces,byusingthenotionofderivativeinthedistributionalsense.ItisalsoshownthatthemappingwhichassociateswithsuchprescribedcurvaturefunctionsthereconstructedcurveisofclassC∞.