maximum-modulus principle

См. также в других словарях:

• Maximum modulus principle — A plot of the modulus of cos(z) (in red) for z in the unit disk centered at the origin (shown in blue). As predicted by the theorem, the maximum of the modulus cannot be inside of the disk (so the highest value on the red surface is somewhere… …   Wikipedia

• Maximum principle — This article describes the maximum principle in the theory of partial differential equations. For the maximum principle in optimal control theory, see Pontryagin s minimum principle. In mathematics, the maximum principle is a property of… …   Wikipedia

• maximum principle — Math. the theorem that a function of a complex variable that is analytic in a domain and on its boundary attains its maximum absolute value on the boundary. Also called maximum modulus principle. * * * …   Universalium

• maximum principle — Math. the theorem that a function of a complex variable that is analytic in a domain and on its boundary attains its maximum absolute value on the boundary. Also called maximum modulus principle …   Useful english dictionary

• Phragmén-Lindelöf principle — In mathematics, the Phragmén Lindelöf principle is a 1908 extension by Lars Edvard Phragmén (1863 1937) and Ernst Leonard Lindelöf of the maximum modulus principle of complex analysis, to unbounded domains. BackgroundIn complex function theory it …   Wikipedia

• List of mathematics articles (M) — NOTOC M M estimator M group M matrix M separation M set M. C. Escher s legacy M. Riesz extension theorem M/M/1 model Maass wave form Mac Lane s planarity criterion Macaulay brackets Macbeath surface MacCormack method Macdonald polynomial Machin… …   Wikipedia

• Schwarz lemma — In mathematics, the Schwarz lemma, named after Hermann Amandus Schwarz, is a result in complex analysis about holomorphic functions defined on the open unit disk. Lemma statementLet D = {z : |z| < 1} be the open unit disk in the complex plane C.… …   Wikipedia

• Blaschke product — In mathematics, the Blaschke product in complex analysis is an analytic function designed to have zeros at a (finite or infinite) sequence of prescribed complex numbers: a 0, a 1, ...inside the unit disc. If the sequence is finite then the… …   Wikipedia

• Auxiliary function — In mathematics, auxiliary functions are an important construction in transcendental number theory. They are functions which appear in most proofs in this area of mathematics and that have specific, desirable properties, such as taking the value… …   Wikipedia

• List of complex analysis topics — Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematics that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied …   Wikipedia

• Nevanlinna theory — is a branch of complex analysis developed by Rolf Nevanlinna. It deals with the value distribution theory of holomorphic functions in one variable, usually denoted z. Nevanlinna theory is very useful when dealing with meromorphic functions as… …   Wikipedia