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...

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

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...

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

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...

Euclidean vector spaces, examples of Hilbert spaces include spaces of square-integrable functions, spaces of sequences, Sobolev spaces consisting of generalized...

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

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

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

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...

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,...

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...

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...

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...

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...

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...

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

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...

mathematical analysis, the Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value...

In complex analysis, the Hardy spaces (or Hardy classes) H p {\displaystyle H^{p}} are spaces of holomorphic functions on the unit disk or upper half...

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 mathematics, a real or complex-valued function f on d-dimensional Euclidean space satisfies a Hölder condition, or is Hölder continuous, when there...

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

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

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...

represent numbers, functions on another space, or subspaces of another space. It is the relationships that define the nature of the space. More precisely...

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

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