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==Comments== |
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* The current version of the introduction "Grunsky matrices, or "Grunsky operatosr" gives the impression that these are the same things under different names. That is not correct. |
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* It seems natural, having named the operators, to say something about the spaces on which those operators are defined. |
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* The introduction mentions the matrices, then the operators, introduces the inequalities, then goes back to the operators in the last couple of sentences. Why not group the concepts together? |
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* The section ''Grunsky inequalities'' states the inequality without explicitly saying that it may or may not hold for the Grunsky matrix of f. This would be a point at which to repeat as a formal statement that the inequality is equivalent to univalence of f. |
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* The section ''Milin's proof of Grunsky inequalities'' again needs to explicitly state what is being proved: here that univalence implies the inequality |
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* Under ''Pairs of univalent functions'' it might help to make clear that in this case the matrix is now doubly infinite. |
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* In ''Unitarity'' the first sentence reads as if it were a definition of unitarity. It needs to be stated explicitly as a theorem. Is it supposed to be obvious, or is the proof to be supplied, or in a reference? Similarly, the second sentence, beginning "So" needs a proof or a reference. "Quasicircle" is not defined in the article, nor is there any article to link it to. The logical status of the rest of the section is not clear: is it intended to prove unitarity, and if so, how exactly does it link to univalence? |
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* Under ''Beurling transform'' T sub Omega appears to change to T sub f without warning. This is especially confusing since f is noit uniquely determined by Omega. Is it the case that T sub f actually depends only on f, or simply that the statements are independent of the choice of f? |
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* Similar remarks apply to "the" Grunsky operator defined as such in the next section. If independent of f, say so explicitly. |
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* The final section ''Singular integral operators on a closed curve'' is clearly incomplete. |
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] (]) 22:11, 19 December 2011 (UTC) |