vector-valued functional

См. также в других словарях:

• Functional (mathematics) — In mathematics, a functional is traditionally a map from a vector space to the field underlying the vector space, which is usually the real numbers. In other words, it is a function that takes a vector as its argument or input and returns a… …   Wikipedia

• Functional equation — In mathematics or its applications, a functional equation is an equation expressing a relation between the value of a function (or functions) at a point with its values at other points. Properties of functions can for instance be determined by… …   Wikipedia

• Holomorphic functional calculus — In mathematics, holomorphic functional calculus is functional calculus with holomorphic functions. That is to say, given a holomorphic function fnof; of a complex argument z and an operator T , the aim is to construct an operator:f(T),which in a… …   Wikipedia

• Spectrum (functional analysis) — In functional analysis, the concept of the spectrum of a bounded operator is a generalisation of the concept of eigenvalues for matrices. Specifically, a complex number λ is said to be in the spectrum of a bounded linear operator T if… …   Wikipedia

• Locally convex topological vector space — In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) which generalize normed spaces. They can be defined as topological vector… …   Wikipedia

• Normed vector space — In mathematics, with 2 or 3 dimensional vectors with real valued entries, the idea of the length of a vector is intuitive and can easily be extended to any real vector space Rn. The following properties of vector length are crucial. 1. The zero… …   Wikipedia

• Linear functional — This article deals with linear maps from a vector space to its field of scalars.  These maps may be functionals in the traditional sense of functions of functions, but this is not necessarily the case. In linear algebra, a linear functional… …   Wikipedia

• Projection-valued measure — In mathematics, particularly functional analysis a projection valued measure is a function defined on certain subsets of a fixed set and whose values are self adjoint projections on a Hilbert space. Projection valued measures are used to express… …   Wikipedia

• Positive linear functional — In mathematics, especially in functional analysis, a positive linear functional on an ordered vector space ( V , ≤) is a linear functional f on V so that for all positive elements v of V , that is v ge;0, it holds that:f(v)geq 0.In other words, a …   Wikipedia

• Generalizations of the derivative — The derivative is a fundamental construction of differential calculus and admits many possible generalizations within the fields of mathematical analysis, combinatorics, algebra, and geometry. Contents 1 Derivatives in analysis 1.1 Multivariable… …   Wikipedia

• Derivative (generalizations) — Derivative is a fundamental construction of differential calculus and admits many possible generalizations within the fields of mathematical analysis, combinatorics, algebra, and geometry. Derivatives in analysis In real, complex, and functional… …   Wikipedia