兩類非對(duì)稱微分算子的幾何結(jié)構(gòu).pdf

1、內(nèi)蒙古大學(xué)碩士學(xué)位論文兩類非對(duì)稱微分算子的幾何結(jié)構(gòu)姓名：楊衛(wèi)華申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：孫炯20030526，塑!!墜旦!～一_——H__———_——●_H—____——_—_●__———_——___——___———p————_———_w_———_——一一G糕oM囂T挺yS譬RUC零UREOFTW0KINDSoFNoNSYMME霉RICDIFF囂R囂N(yùn)TIALopERA茁oRSABSTRACTNonselfadjoint

2、quasidifferentialexpressionManditsformaladjointM十maygeneratednonsymmetricdifferentialoperatorsAlthoughminimaloperatorsTo，霄generatedbyM，M十a(chǎn)renotsymmetric，formanadjointpairInthispaperlwestudy，intwokindsofconditions，regular

3、lysolvableoperatorswithrespecttothisadjointpairTo，霄andgivetheirgeometrydescriptioninthefollowingways。Bythemapft《——露(8)《＆】——《)，啪buildisomorphismsbetweenquotientspacesD(T)／D(To)，D(T)／D(對(duì))and08(quotientspaces掃《D／D(To)，D(T)／

4、D(T2)andCe)BecauseGreenfomulasdefinedin口F)，D(T)areintermofboundaryvalues，thereforeshowassymplecticforms睦(【：】2)ofg“(0加)，andwegetsympleticcomplexvectorspaces(G4，‰)((g加，1：12))Thus，symplecticgeometryisappliedfordescriptionso

5、fregularlyso玨ableoperatorsintwokindsofconditions，andweprovedthereexistsonetoonecorrespondencerelationshipbetweenregularlysolvableoperatorsandorthodoxypairsofsymplecticspaces，F(xiàn)inallyinanexample，bysolvingMu=Au，M“=蛔inL2(。，砷