Q. on Mittag Leffler theorem and analytic sheaf cohomology

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SUMMARY

The Mittag-Leffler theorem can be applied to express the function e^{1/sin z} as the sum of two analytic functions, f and g. Function f is analytic in the region where Re(z) > π/2, while g is analytic in the region where Re(z) < π. This surprising result is documented in Lars Hormander's book, "An Introduction to Complex Analysis in Several Variables." The proof of this theorem is straightforward, although prior proofs may require additional reading.

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  • Understanding of the Mittag-Leffler theorem
  • Familiarity with analytic functions
  • Knowledge of complex analysis, specifically in several variables
  • Basic concepts of function regions in the complex plane
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  • Study the Mittag-Leffler theorem in detail
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  • Investigate the properties of e^{1/sin z} in different regions of the complex plane
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lark
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See http://camoo.freeshell.org/cohomquest.pdf"
thanks
Laura
 
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The answer is yes, you could express [tex]e^{1/sin z}[/tex] as [tex]f+g[/tex], [tex]f[/tex] analytic in [tex]Re(z)>\pi/2[/tex] and [tex]g[/tex] analytic in [tex]Re(z)<\pi[/tex]! Pretty surprising, but I looked it up in Lars Hormander's book "An introduction to complex analysis in several variables". The proof isn't all that difficult, tho I didn't read the proofs before that one.
Laura
 

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