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...

{\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 ...

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...

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...

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

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 ∪ { ∞...

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...

The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is...

manifold M: any holomorphic function on it is constant by the maximum modulus principle. Now if we had a holomorphic embedding of M into Cn, then the...

{\displaystyle U} was arbitrary, the function f {\displaystyle f} is open. Maximum modulus principle Rouché's theorem Schwarz lemma Open mapping theorem (functional...

)^{N}}}\leq {\frac {M}{(y_{0}+\lambda )^{N}}}} . Applying maximum modulus principle to the function g ( z ) = f ( z ) ( z + i λ ) N {\displaystyle...

here referring to an algebraic property of a number. Using the maximum modulus principle Lang also found a separate way to estimate the absolute values...

f(z)=\int |g|^{pz}|h|^{q(1-z)}.} Riesz–Thorin theorem Phragmén–Lindelöf principle Hadamard, Jacques (1896), "Sur les fonctions entières" (PDF), Bull. Soc...

of a material is quantified by the elastic modulus such as the Young's modulus, bulk modulus or shear modulus which measure the amount of stress needed...

measures the resonant frequencies in order to calculate the Young's modulus, shear modulus, Poisson's ratio and internal friction of predefined shapes like...

here referring to an algebraic property of a number. Using the maximum modulus principle, Lang also found a separate estimate for absolute values of derivatives...

supports E {\displaystyle E} = modulus of elasticity I {\displaystyle I} = area moment of inertia of cross section The maximum elastic deflection on a beam...

Where defined it is injective. It is holomorphic on D. By the maximum modulus principle, to show that g maps D onto D it suffices to show it maps S onto...

well-defined contractive extension to the semigroup follows from the maximum modulus principle and the fact that the semigroup operators are closed under adjoints...

m {\displaystyle E_{m}} is the elastic modulus of the matrix E f {\displaystyle E_{f}} is the elastic modulus of the fibers Fibers are commonly arranged...

modular_pow(base, exponent, modulus) is if modulus = 1 then return 0 c := 1 for e_prime = 0 to exponent-1 do c := (c * base) mod modulus return c A third method...

tendons have a maximum modulus of approximately 800 MPa; thus, any additional loading will not result in a significant increase in modulus strength. These...

c can be reduced to only two independent numbers, the bulk modulus K and the shear modulus G, that quantify the material's resistance to changes in volume...

been manufactured and distributed widely with a modulus of 141.5 instead of the Baumé scale modulus of 140. The scale was so firmly established that...

pure topological results about analytic functions (such that the Maximum Modulus Principle, Rouché's theorem etc.) extend to quasiregular maps. Injective...

{\displaystyle M} is called the modulus of elasticity (or just modulus) while its reciprocal J {\displaystyle J} is called the modulus of compliance (or just compliance)...

{\displaystyle z} there is a term of maximal modulus. This term depends on r := | z | {\displaystyle r:=|z|} . Its modulus is called the maximal term of the series:...