有关全纯映照子族的两类Roper-Suffridge算子.pdf

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4、nÙ.31˜Ù,·‚{‡0õECêAÛ¼êØuе,©¤^˜PÒÚ½Â,±9©̇(J.31Ù,·‚ÄkÚ˜aí2Roper-SuridgeŽfF(z)=(f(z)+f0(z)11Pn11azpk;f0(z)p2z;:::;f0(z)pnz)0,,y²3˜½^‡eTŽf3Em¥kk121nk=2PnReinhardt•=fz=(z;:::;z)2Cn:jzj2+jzjpk<1;p2N+;k=n;p2;:::;pn1n1kkk=22;:::;n:gþ±g’.Ú/5,g.Ú/59r.Ú/5.

5、31nÙ,·‚E,˜aRoper-SuridgeŽfF(z)==((f(z1))1z;n;1;:::;nz11:::;(f(z1))nz)0,Ù¥2[0;1];k=1;:::;n,…;j=2;:::;n;? ©Oy²z1nkj1Ù3Bn,9Reinhardt•þ±(/5.n;p1;:::;pn©Ì‡´é®k(J?1ïÄÚí2,¿˜#(Ø,l¦·‚éRoper-SuridgeŽfk•?˜Ú@£.'…c:Roper-SuridgeŽf,VXNì,Reinhardt•IABSTRACTTheRo

6、per-Suridgeoperatorplaysanimportantroleinconstructingthebiholomor-phicmappingsofseveralcomplexvariablesfromtheunivalentfunctionsofonecomplexvariable.Inthispaper,wemainlystudysomepropertiesofthetwoclassesofRoper-Suridgeoperatorforholomorphicmappingsondierentdomain

7、s.Thewholethesiscontainsthreechapters.Intherstchapter,webrie yintroducethedevelopmentbackgroundofthegeometricfunctiontheoryinseveralcomplexvariables,somenotations,denitions,andthemainresultsofthisarticle.Inthesecondchapter,rstly,weintroduceaclassofgeneralizedRope

8、r-Suridgeop-Pn11eratorgivenbyF(z)=(f(z)+f0(z)azpk;f0(z)p2z;:::;f0(z)pnz)0.Secondly,we11kk121nk=2arguethattheoperatorcanpreservethepropert