TEAM PROJECT. Maximum Modulus of Analytic Functions. (a)
Chapter 18, Problem 18.6(choose chapter or problem)
TEAM PROJECT. Maximum Modulus of Analytic Functions. (a) Verify Theorem 3 for (i) F(:::) = ::2 and the square 4 ~ x ~ 6. 2 ~ Y ~ 4, (ii) F(:::) = e1z and any bounded domain. (iii) F(:::) = sin:: and the unit disk. (b) F(x) = cos x (x real) has a maximum I at O. How does it follow that this cannot be a maximum of IFez.) I = Icos:::1 in a domain containing Z = O? (c) F(::) = 1 + 1::12 is not Lero in the disk Izi ~ 4 and has a minimum at an interior point. Does this contradict Theorem 3? (d) If F(:::) is analytic and not constant in the closed unit disk D: 1
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