In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is...

the function spaces of wave functions. In this case, the wave functions are square integrable. One can initially take the function space as the space of...

square-integrable function, also called a quadratically integrable function or L 2 {\displaystyle L^{2}} function or square-summable function, is a real- or...

mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes...

or bicontinuous function, is a bijective and continuous function between topological spaces that has a continuous inverse function. Homeomorphisms are...

of topological vector spaces, which include function spaces, inner product spaces, normed spaces, Hilbert spaces and Banach spaces. In this article, vectors...

vector spaces to spaces that may be infinite-dimensional. Hilbert spaces arise naturally and frequently in mathematics and physics, typically as function spaces...

term "Banach space" and Banach in turn then coined the term "Fréchet space". Banach spaces originally grew out of the study of function spaces by Hilbert...

mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the...

In mathematics, a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as a...

sublinear function (or functional as is more often used in functional analysis), also called a quasi-seminorm or a Banach functional, on a vector space X {\displaystyle...

In complex analysis, the Hardy spaces (or Hardy classes) Hp are certain spaces of holomorphic functions on the unit disk or upper half plane. They were...

Exponential object, category-theoretic equivalent First-class function Function space, set-theoretic equivalent Pierce, Benjamin C. (2002). Types and...

mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function together with its derivatives...

function whose domain is the unit interval [0, 1]. In the most general form, the range of such a function may lie in an arbitrary topological space,...

natural function f for which the theorem is true. Time-constructible functions are often used to provide such a definition. Space-constructible functions are...

, the vector space of essentially bounded measurable functions with the essential supremum norm, are two closely related Banach spaces. In fact the former...

metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a...

In mathematical analysis, a function of bounded variation, also known as BV function, is a real-valued function whose total variation is bounded (finite):...

\mathbb {R} ^{n}} . (Bump functions are examples of test functions.) The set of all such test functions forms a vector space that is denoted by C c ∞ (...

Schwartz space S {\displaystyle {\mathcal {S}}} is the function space of all functions whose derivatives are rapidly decreasing. This space has the important...

theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves the structure of the spaces: the preimage of...

a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements...

a bump function (also called a test function) is a function f : R n → R {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} } on a Euclidean space R n {\displaystyle...

the space. Prominent examples of function spaces with some notion of convergence are Lp spaces and Sobolev space. Suppose f is a real-valued function and...

basis for some function space of interest, hence the name. Sums of radial basis functions are typically used to approximate given functions. This approximation...

mathematics, orthogonal functions belong to a function space that is a vector space equipped with a bilinear form. When the function space has an interval as...

maps a function from its original function space into another function space via integration, where some of the properties of the original function might...

M-theory (7D hyperspace + 4D), and the state-space of quantum mechanics is an infinite-dimensional function space. The concept of dimension is not restricted...

In mathematical analysis, the spaces of test functions and distributions are topological vector spaces (TVSs) that are used in the definition and application...