In mathematics, Hardy's theorem is a result in complex analysis describing the behavior of holomorphic functions.
Let be a holomorphic function on the open ball centered at zero and radius in the complex plane, and assume that is not a constant function. If one defines
for then this function is strictly increasing and is a convex function of .
See also
References
- John B. Conway. (1978) Functions of One Complex Variable I. Springer-Verlag, New York, New York.
This article incorporates material from Hardy's theorem on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.
🔥 Top keywords: Main PageShannen DohertySpecial:SearchCarlos AlcarazList of United States presidential assassination attempts and plotsAttempted assassination of Donald TrumpDonald TrumpRichard Simmons2024 shooting at a Donald Trump rallyLamine YamalNovak DjokovicNico WilliamsUEFA European ChampionshipWikipedia:Featured picturesThomas Matthew CrooksProject 2025Attempted assassination of Ronald ReaganUEFA Euro 2024Jacoby JonesAR-15–style rifleMukesh AmbaniLonglegsSpain national football teamKimberly CheatleKalki 2898 ADList of Wimbledon gentlemen's singles championsCole PalmerGareth SouthgateJohn Hinckley Jr.Harry KaneLuke PerryAntifa (United States)United States Secret Service.xxxDeaths in 2024Ruth WestheimerEvan VucciButler, PennsylvaniaIndian 2