ropersuffridge算子的系数估计和偏差定理-coefficient estimation and deviation theorem of ropersuffridge operator.docx
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ropersuffridge算子的系数估计和偏差定理-coefficient estimation and deviation theorem of ropersuffridge operator
?????◆照??数??和?????多???数论???⑤?部?, ? Roper-Suffrid-ge ????单??数????数??多??数????◆照?起????????. ????多??数?????, ????殊?? Cn ??单?? Bn 上????????? F (z) ?研?对?, ?单???上????数???研?这???? n = 2 ???数?? 和????.?????章.??????章, ??④?????多???何?数论??展??, ????????记号, ????, ??????????.???章, ???单?????④②??? n = 2 ??? F (z) ???????数??.???章, ???单???上????数????????? n = 2 ??? F (z) ?????, ???②?? n = 1 ????????单??????数????????.????????对???论???研?和推?, ??????★??◆, ?????对??◆照??数??和?????????步???.???:?数??, ????, 推?? Roper-Suffridge ??, ??◆照IABSTRACTThe estimate of the coefficient and the distortion theorem of biholomorphic mappings play an important role in function theory of several complex variables; in this thesis,we study a special class of biholomorphic starlike mappings F (z) which keep the property of starlikeness in Bn. From the starlikeness function, we discuss the estimation of homogeneous expansion and the distortion theorem of the operator F (z) during the two dimensions. The whole thesis contains three chapters.In the first chapter, we introduce briefly the background of the development of the geometric function theory in several complex variables, some notations, basic concepts, definitions and the main results of the thesis.In the second chapter, we prove the estimate of the coefficient of the operator F (z) which we use the method which comes from the one complex variable and obtain some new results.In the third chapter, we prove the distortion of the operator F (z) during the two dimensions, we also use the method which comes from the one complex variable. Then we prove that the result can come back to the situation of the one dimension.The main results of this thesis are based on the known results, but extend and improve them. So we have a deep realization about the estimation of the coefficient and the distortion theorem of the starlike mapping F (z).KEY WORDS:the estimate of the coefficient, distortion theorem, Roper-Suffridge exten- sion operator, starlike mappingsIII关于学位论文
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