Liouville's theorem
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Suppose that f(z) = u(x , y) + i*v(x, y) (where z = x + i*y) is ENTIRE and not constant. Use Liouville's theorem to prove that v(x, y) is unbounded. Under what conditions can a function that is harmonic everywhere be bounded?
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Solution Summary
Liouville's theorem is applied.
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Proof:
Let . Since is entire, then is also entire.
I claim that is unbounded.
If is bounded, ...
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