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Timeline for Finding a particular matrix factor

Current License: CC BY-SA 4.0

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Jun 26, 2018 at 19:20 vote accept Ludwig
Jun 26, 2018 at 15:47 comment added Alex Gavrilov For $|x|\le 1$ the function $a(x)$ is analytic by the assumption (1), and $a(x^{-1})$ is analytic because numerator and denominator are analytic and the latter is not zero.
Jun 26, 2018 at 15:43 comment added Alex Gavrilov Without (2) the argument doesn't work because the denominator could turn zero.
Jun 26, 2018 at 14:56 comment added Ludwig Thanks for the answer! Could you please elaborate a little more on your sentence "assuming (1) and (2), the function $a(x)$ would be analytic both for $|x|\le 1$ and for $|x|\ge 1$"? In particular, how is requirement (2) applied here?
Jun 26, 2018 at 12:32 history answered Alex Gavrilov CC BY-SA 4.0