1. Suppose that f(z) is analytic on 0 < |z| < ∞ and there exists a f(z) nonnegative integer m such that is bounded on 0<|z|<∞. Prove that there exists a constant c such that f(z) = czm on 0<|z|<∞. zm

1. Suppose that f(z) is analytic on 0 < |z| < ∞ and there exists a f(z) nonnegative integer m such that is bounded on 0<|z|<∞. Prove that there exists a constant c such that f(z) = czm on 0<|z|<∞. zm

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.4: Ordered Integral Domains

Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....

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1. Suppose that f(z) is analytic on 0 < |z| < ∞ and there exists a
f(z)
nonnegative integer m such that is bounded on 0<|z|<∞. Prove
that there exists a constant c such that f(z) = czm on 0<|z|<∞.
zm
C

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