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...

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...

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...

of radius r {\displaystyle r} centered at the origin, then the maximum modulus principle implies that, for r < 1 {\displaystyle r<1} , given any z ∈ D...

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

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...

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...

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

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 ∪ { ∞...

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

describe a material's response to stress, along with the shear modulus and Young's modulus. buoyancy Contents:  Top 0–9 A B C D E F G H I J K L M N O P...

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

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

)^{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...

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...

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...

tending to lengthen an object. Tensile modulus Young's modulus E {\displaystyle E} , the Young modulus, or the modulus of elasticity in tension, is a mechanical...

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

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...

vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance...

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

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

shear modulus describes the response to shear, and Young's modulus describes the response to linear stress. For a fluid, only the bulk modulus is meaningful...

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

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...

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...

where k {\displaystyle k} is the material bulk modulus. Following the same approach the micro-modulus constant c {\displaystyle c} can be extended to...