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5 votes
3 answers
391 views

Does the rate of decay of an entire function dictate the global growth rate?

If $f$ is entire and we assume a decay rate on $\mathbb{R}^+$, does this dictate a growth rate on $\mathbb{C}$? For example, is there a function that decays as $e^{-x^2}$ on $\mathbb{R}^+$ and is of …
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  • 503
0 votes
0 answers
56 views

Questions on the behaviour of functions of exponential type 1

I am interested in understanding the properties of entire functions of exponential type 1. I have few questions about their growth. How many sectors can a function of exponential type have, in which …
tst's user avatar
  • 503