Let p: U → C be a holomorphic function on the star-shaped open set U. Suppose also p′(z) is continuous. Show that there exists a holomorphic function t: U → C such that p(z) = exp(t(z)) for all z ∈ U. Also show that t(z) is unique up to the addition of a constant 2πik, k ∈ Z. Use the complex FTC to prove this existence

Let p: U → C be a holomorphic function on the star-shaped open set U. Suppose also p′(z) is continuous. Show that there exists a holomorphic function t: U → C such that p(z) = exp(t(z)) for all z ∈ U. Also show that t(z) is unique up to the addition of a constant 2πik, k ∈ Z. Use the complex FTC to prove this existence

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...

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