A graduate course on complex analysis, equivalent to an incoming graduate student one-semester (or a bit more) class.
We prove the Arzelà-Ascoli theorem, that is, on a compact metric space, an equicontinuous pointwise bounded sequence of functions has a subsequence that converges uniformly. We also prove a version of this theorem for open subsets of the complex plane getting uniform convergence on compact subsets. (Subsection 6.1.3 in the book).
The course is based on the book "Guide to Cultivating Complex Analysis", which is available freely online at
www.jirka.org/ca/
(You can also buy an inexpensive paperback copy, the best way to support this project)
See the course playlist: • Cultivating Complex An...
Негізгі бет 56. Arzelà-Ascoli (Cultivating Complex Analysis 6.1.3)
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