MathDB
rational function

Source: Miklos Schweitzer 2005 q9

August 27, 2021
complex numbersinequalitiesrational functioncomplex analysis

Problem Statement

prove that if rnr_n is a rational function whose numerator and denominator have at most degrees nn, then ∣∣rn∣∣1/2+∥1rn∥2≥12n−1||r_n||_{1/2}+\left\|\frac{1}{r_n}\right\|_2\geq\frac{1}{2^{n-1}} where ∣∣⋅∣∣a||\cdot||_a denotes the supremum over a circle of radius aa around the origin.
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