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...

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

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

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

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

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...

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

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...

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...

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

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...

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

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 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...

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

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...

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...

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...

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...

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

supported smooth functions on a Euclidean space are called bump functions. Mollifiers are an important special case of bump functions as they can be used...

of a linear operator D defined on some function space is any non-zero function f {\displaystyle f} in that space that, when acted upon by D, is only multiplied...

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

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

and statistics, a probability mass function (sometimes called probability function or frequency function) is a function that gives the probability that a...

coefficients in F is vector space over F denoted F[x1, x2, ..., xr]. Here r is the number of variables. See main article at Function space, especially the functional...

values of functions are real and complex numbers. The concept has been generalized to functions between metric spaces and between topological spaces. The latter...

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...

coordinate space C n . {\displaystyle \mathbb {C} ^{n}.} Sometimes such a domain is used as the domain of a function, although functions may be defined...