Commune · Savoirs

Maximum modulus principle

Theorem that a holomorphic function’s absolute value cannot reach a strict local maximum at the interior of its domain

Texte en anglais

In mathematics, the maximum modulus principle in complex analysis states that if f {\displaystyle f} is a holomorphic function, then the modulus | f | {\displaystyle |f|} cannot exhibit a strict maximum that is strictly within the domain of f {\displaystyle f} . In other words, either f {\displaystyle f} is locally a constant function, or, for any point z 0 {\displaystyle z_{0}} inside the domain of f {\displaystyle f} there exist other points arbitrarily close to z 0 {\displaystyle z_{0}} at which | f | {\displaystyle |f|} takes larger values.

Sur Wikipédia

Texte en anglais Pas encore d'article dans ta langue : extrait en anglais.

In mathematics, the maximum modulus principle in complex analysis states that if f {\displaystyle f} is a holomorphic function, then the modulus | f | {\displaystyle |f|} cannot exhibit a strict maximum that is strictly within the domain of f {\displaystyle f} . In other words, either f {\displaystyle f} is locally a constant function, or, for any point z 0 {\displaystyle z_{0}} inside the domain of f {\displaystyle f} there exist other points arbitrarily close to z 0 {\displaystyle z_{0}} at which | f | {\displaystyle |f|} takes larger values.

Texte : Wikipédia en anglais, CC BY-SA 4.0. · Image : Oleg Alexandrov (Public domain) ·

Cartes voisines

Ouvrir

…

Touche pour fermer

Confirmation