mathematics, the maximum modulus principle in complex analysis states that if f {\displaystyle f} is a holomorphic function, then the modulus | f | {\displaystyle...

of the maximum modulus principle, which is only applicable to bounded domains. In the theory of complex functions, it is known that the modulus (absolute...

maximum principle is one of the most useful and best known tools of study. Solutions of a differential inequality in a domain D satisfy the maximum principle...

may be bounded by its real part. It is an application of the maximum modulus principle. It is named for Émile Borel and Constantin Carathéodory. Let...

{\displaystyle |a|=1} . The proof is a straightforward application of the maximum modulus principle on the function g ( z ) = { f ( z ) z if  z ≠ 0 f ′ ( 0 ) if ...

does not require the maximum modulus principle (in fact, a similar argument also gives a proof of the maximum modulus principle for holomorphic functions)...

differential equations and the Phragmén–Lindelöf principle, one of several refinements of the maximum modulus principle that he proved in complex function theory...

space of a commutative Banach algebra where an analog of the maximum modulus principle holds. It is named after its discoverer, Georgii Evgen'evich Shilov...

disk and has a maximum at φ ( p 0 ) ∈ D {\displaystyle \varphi (p_{0})\in \mathbb {D} } , so it is constant, by the maximum modulus principle. Let C ∪ { ∞...

theorem Hadamard three-circle theorem Hardy space Hardy's theorem Maximum modulus principle Nevanlinna theory Paley–Wiener theorem Progressive function Value...