Maximum modulus principle
en.wikipedia.org · 857 words · saved by 1 readers
In mathematics, the maximum modulus principle in complex analysis states that if
From Wikipedia, the free encyclopedia A plot of the modulus of (in red) for in the unit disk centered at the origin (shown in blue). As predicted by the theorem, the maximum of the modulus cannot be inside of the disk (so the highest value on the red surface is somewhere along its edge). In mathematics, the maximum modulus principle in complex analysis states that if is a holomorphic function, then the modulus cannot exhibit a strict maximum that is strictly within the domain of . In other words, either is locally a constant function, or, for any point inside the domain of there exist…
saved by
related reading
- Sobolev inequality - Wikipediaen.wikipedia.org
- Napkin.pdfvenhance.github.io
- Lipschitz continuityen.wikipedia.org
- Rouché's theorem - Wikipediaen.wikipedia.org
- Analytic continuationen.wikipedia.org
- Analytic function - Wikipediaen.wikipedia.org
- Zeros and poles - Wikipediaen.wikipedia.org
- Fundamental theorem of algebra - Wikipediaen.wikipedia.org
- Heine–Cantor theorem - Wikipediaen.wikipedia.org
- Maximum and minimum - Wikipediaen.wikipedia.org
- Complex Differentiationcomplex-analysis.com
- Mandelbrot set - Wikipediaen.wikipedia.org