[引用][C] Convolutory operators preserving univalent functions
YE Khokhlov - Ukrainian Mathematical Journal, 1985 - Springer
Ukrainian Mathematical Journal, 1985•Springer
I. Introduction. The univalent normed conformal mappings of the unit disk U={z 6 9: Izl< I}
form a complex nonlinear compactumS, lying in thelinear topological space~ of hoiomorphic
functions. The impossibility of carrying linear structures from~ over to S (a linear combination
of univalent functions can even be infinitely sheeted) complicates the construction of
variations of univalent functions, the solution of extremal problems, obtaining integral
representations, etc. Therefore, the determination of objects and structure in S with a linear …
form a complex nonlinear compactumS, lying in thelinear topological space~ of hoiomorphic
functions. The impossibility of carrying linear structures from~ over to S (a linear combination
of univalent functions can even be infinitely sheeted) complicates the construction of
variations of univalent functions, the solution of extremal problems, obtaining integral
representations, etc. Therefore, the determination of objects and structure in S with a linear …
I. Introduction. The univalent normed conformal mappings of the unit disk U={z 6 9: Izl< I} form a complex nonlinear compactumS, lying in thelinear topological space~ of hoiomorphic functions. The impossibility of carrying linear structures from~ over to S (a linear combination of univalent functions can even be infinitely sheeted) complicates the construction of variations of univalent functions, the solution of extremal problems, obtaining integral representations, etc. Therefore, the determination of objects and structure in S with a linear character is a very important and nontrivial problem.
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