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Homework 4

HWK 4 problems

Hint for IV.6.3 --Steve Bell

We assume $ (f)''=f $ on $ \mathbb C $.

Notice that

$ (e^z f)''=e^zf +2e^zf'+e^zf''=2(e^zf + e^zf')=2(e^zf)'. $

Let $ g=e^zf. $ Then $ g'=2g $ and now you can use the theorem from class that concerns solutions of this first order complex ODE. By the way, you will also need to use the fact that if two analytic functions on the complex plane have the same derivative, then they must differ by a constant.

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Ph.D. on Applied Mathematics in Aug 2007. Involved on applications of image super-resolution to electron microscopy

Francisco Blanco-Silva