Show that $\Delta \log (|f(z)|)=0$, where $f(z)$ is an analytic function.
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 1342 views
- $2.00
Related Questions
- Derive the solution $u(x,t)=\frac{x}{\sqrt{4 \pi}} \int_{0}^{t} \frac{1}{(t-s)^{3/2}}e^{\frac{-x^2}{4(t-s)}}g(s) \, ds$ for the heat equation
- Week solution of the equation $u_t + u^2u_x = f(x,t)$
- Suppose $u \in C^2(\R^n)$ is a harmonic function. Prove that $v=|\nabla u|^2$ is subharmonic, i.e. $-\Delta v \leq 0$
- Evaluate $\frac{1}{2 \pi i}\int_{|x|=1} \frac{z^{11}}{12z^{12}-4z^9+2z^6-4z^3+1}dz$
- Find solutions to the Riemann Problems
- Use Rouche’s Theorem to show that all roots of $z ^6 + (1 + i)z + 1 = 0$ lines inside the annulus $ \frac{1}{2} \leq |z| \leq \frac{5}{4}$
- Find a formula for the vector hyperbolic problem
- Maximum principle for the heat equation involving an aditional linear term