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Hello. Are there any generalisations of the Weierstrass factorization theorem? If so, where can I find information about this?

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There is a tightening of this called Hadamard's factorization theorem. What kind of generalization do you have in mind? Are you looking for generalization in higher dimensions? – timur May 19 2012 at 19:12
With additional details this could be a good question. In the present form it is IMO not a real question; vote to close. – quid May 19 2012 at 23:20

closed as not a real question by Will Sawin, Steven Landsburg, quid, S. Sra, Bill Johnson May 20 2012 at 3:51

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What do you need this generalization for? Is it just curiosity? The proof of this theorem via first Cousin problem generalizes to sheaf cohomology. The corresponding theorem is true for noncompact Riemann surfaces because they are all Stein manifolds, and thus have vanishing coherent analytic sheaf cohomology.

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Thanks for your reply. It is good to have someone post a helpful comment rather than close the discussion. I would like to investigate some infinite products of the form: $\prod_{k=1}^\infty f(z)^{k^a}e^{g(z)}$, which I know to be similar to the infinite product of the sin function when we use the WFT. – pbs May 20 2012 at 10:47

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