Liouville’s theorem states that every entire function that is bounded also has this property. For 10 points each:
[10m] Identify this property of functions whose Fourier transform is a delta function at the origin.
ANSWER: constant [accept equivalents mentioning that the function’s value does not change]
[10e] A constant function will have only one term when represented as one of these series named for a British mathematician. When these series are centered on zero, they’re called Maclaurin series.
ANSWER: Taylor series
[10h] If a function is non-constant and entire, its range spans at least the whole complex plane minus one point according to this mathematician’s “little theorem.” It’s not Cauchy, but this mathematician also names a theorem with Ernst Lindelöf that characterizes the unique solution of initial value problems.
ANSWER: Émile Picard [or Charles Émile Picard; accept Picard’s little theorem or Picard-Lindelöf theorem]
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