Abstract
One of the most important things that we do in complex function theory is to construct holomorphic functions with specified properties. Given the way that we are prone to think, a natural way to effect this process is to perform some local construction and then to endeavor to extend the result to an entire domain Ω The function theory of one complex variable is replete with methods for performing that “extension” process. Infinite products, analytic continuation, division problems, approximation theorems (Runge, Mergelyan), and the Cauchy—Riemann equations are just some of the devices that we have for taking a local construction and making it global.
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© 2006 Birkhäuser Boston
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(2006). Cousin Problems, Cohomology, and Sheaves. In: Krantz, S.G. (eds) Geometric Function Theory. Cornerstones. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4440-7_13
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DOI: https://doi.org/10.1007/0-8176-4440-7_13
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4339-3
Online ISBN: 978-0-8176-4440-6
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