Title: Maximum Modulus Principle -- from Wolfram MathWorld
Open Graph Title: Maximum Modulus Principle -- from Wolfram MathWorld
X Title: Maximum Modulus Principle -- from Wolfram MathWorld
Description: Let U subset= C be a domain, and let f be an analytic function on U. Then if there is a point z_0 in U such that |f(z_0)|>=|f(z)| for all z in U, then f is constant. The following slightly sharper version can also be formulated. Let U subset= C be a domain, and let f be an analytic function on U. Then if there is a point z_0 in U at which |f| has a local maximum, then f is constant. Furthermore, let U subset= C be a bounded domain, and let f be a continuous function on the closed set U^_...
Open Graph Description: Let U subset= C be a domain, and let f be an analytic function on U. Then if there is a point z_0 in U such that |f(z_0)|>=|f(z)| for all z in U, then f is constant. The following slightly sharper version can also be formulated. Let U subset= C be a domain, and let f be an analytic function on U. Then if there is a point z_0 in U at which |f| has a local maximum, then f is constant. Furthermore, let U subset= C be a bounded domain, and let f be a continuous function on the closed set U^_...
X Description: Let U subset= C be a domain, and let f be an analytic function on U. Then if there is a point z_0 in U such that |f(z_0)|>=|f(z)| for all z in U, then f is constant. The following slightly sharper version can also be formulated. Let U subset= C be a domain, and let f be an analytic function on U. Then if there is a point z_0 in U at which |f| has a local maximum, then f is constant. Furthermore, let U subset= C be a bounded domain, and let f be a continuous function on the closed set U^_...
Opengraph URL: https://mathworld.wolfram.com/MaximumModulusPrinciple.html
Domain: mathworld.wolfram.com
| DC.Title | Maximum Modulus Principle |
| DC.Creator | Weisstein, Eric W. |
| DC.Description | Let U subset= C be a domain, and let f be an analytic function on U. Then if there is a point z_0 in U such that |f(z_0)|>=|f(z)| for all z in U, then f is constant. The following slightly sharper version can also be formulated. Let U subset= C be a domain, and let f be an analytic function on U. Then if there is a point z_0 in U at which |f| has a local maximum, then f is constant. Furthermore, let U subset= C be a bounded domain, and let f be a continuous function on the closed set U^_... |
| DC.Date.Created | 2000-06-20 |
| DC.Subject | 26 |
| DC.Rights | Copyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement. |
| DC.Format | text/html |
| DC.Identifier | https://mathworld.wolfram.com/MaximumModulusPrinciple.html |
| DC.Language | en |
| DC.Publisher | Wolfram Research, Inc. |
| DC.Relation.IsPartOf | https://mathworld.wolfram.com/ |
| DC.Type | Text |
| Last-Modified | 2000-06-20 |
| og:image | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_MaximumModulusPrinciple.png |
| og:type | website |
| twitter:card | summary_large_image |
| twitter:image:src | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_MaximumModulusPrinciple.png |
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