關于抽象函數(shù)逼近的幾個問題.pdf

1、江西師范大學碩士學位論文關于抽象函數(shù)逼近的幾個問題姓名：聶紅隆申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：葉中秋2003.3.1關于抽象函數(shù)逼近的幾個問題AbstractInthisthesisweinwstigateseveralproblemsconcerningapproximationofabsUactfunctiomInchapter2，We：definetheabstractperiodicthreelcvolboundedv

2、ariationfunctionswillarangeinaBanachspaceEandstudythepropellyOnapproximatingitbytrigonometricpolynomialswithabslracteoettiei鋤tsfromEFinallythefollowing撐proved：theorderofapproximationforxq)∈嚏bytlIepolynomialsandthe#ufliei

3、cntandnocc黜atyconditionofx(t)∈咳Inchapter3，t虹plq》口略ofapproximatiorLof答me豫In隘繹髓iodic鈿o1眥lboundedvariationfimetion，0)isdiscussedandthat，(cost)isaperiodietwolevelboundodvariationfunctionisprovedSecondlythefollowingisobtained

4、：the∞d釬ofapproximalionforf(x)GrE2_刪坶mepolynomialsandllaesufficientandneecssarycondition0f，0)∈K!啪Furthcrmore，WcobtainlllOretnvcisec武imateofapproximationfor，0)∈Vr2111bythealgebrapolynomialsand血csutIieientconditionoff(x)e％1

5、】Inchapter4，w弓stuay位pl_o】嗍of∞刪vectorpolynomial暑h180c101“1，WCdefmetheclassofchebystlwtype1∞ectorpolynomialsanddiscuss缸extremalpropertyforClacbyshevtypevc(：torpolynomialsItisprovedthattheChebyshcvtypevectorpDl)IIImIlialsam

6、alsotheleastdoviafionfunctiomanduniqueinthecI刪％=I(fl(x)，，2(x)，厶(x))IZ∈c黜1】z‘”’(x)≥Lxe[I11withsortieilOmlqInsector2WOdefmctheclassPLandstudytheinequalitiesforderivativesofLorentztypevectorpolynomialsinB(p，cOnormAslrongere

7、stimateoflli曲cfderivativesforPLisobtainedIn$1：CtOl“3，weextendatheoremofVarmatoB(p，q)normforlBolneclassofvectorpolynomialsandobtaintWOsimilarresultsKeyWortls：abstractfunction；Periodicthreelevelboundedvariationfunction；two