Hill functions are the unique maximizers of sharpness (n/4) among degree-n rational functions obeying 0 ≤ α_i ≤ β_i.
The linear framework
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Sharpness characterizes Hill functions
Hill functions are the unique maximizers of sharpness (n/4) among degree-n rational functions obeying 0 ≤ α_i ≤ β_i.