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...

attributed to Erhard Schmidt, 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)...

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...

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

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

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 ∪ { ∞...

{\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...

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...

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...

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...

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...

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

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

small-scale shear modulus in any direction, not to any rigidity or stiffness properties such as its bulk modulus or Young's modulus. Stiffness is often...

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...

resistance to change in shape. A superhard material has high shear modulus, high bulk modulus, and does not deform plastically. Ideally superhard materials...

controlled by the material properties in terms of density and modulus (stiffness). The density and modulus, in turn, vary according to temperature, composition...

complex modulus G*. The elastic contribution is the storage modulus G’, which is equal to G*cosδ, while the viscous contribution is the loss modulus G”, which...

index modulo k is r, nor by any vertical line whose index modulu k is s. By the pigeonhole principle, there is at least one pair (r,s) such that | M D S (...

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...