Function Space

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function space

[′fəŋk·shən ‚spās]
A metric space whose elements are functions.

Function Space


a set of functions for which there is defined a notion of distance or, more generally, of proximity between any two functions. A function space is called linear if, along with any two elements f1 and f2 it contains all their linear combinations αf1, + βf2, where α and β are real or complex numbers. An example of a linear function space is the space C(a, b) of all continuous functions on the interval [a, b] with the distance p(f1, f2) between two functions being given by the formula

Function spaces are the most important concrete linear spaces studied in functional analysis. [28–388–1 ]

References in periodicals archive ?
Their topics include the measurability and semi-continuity of multifunctions, the optimality of function spaces in Sobolev embeddings, a note on the off-diagonal Muckenhoupt-Wheedon conjecture, the Radon-Nikod<'y>m theorem for vector measures and integral representation of operators on Banach function spaces, and the Orlicz-Pettis theorem for multiplier convergent series.
To be precise, we study p-concavity, type and cotype of multipliers from Banach function spaces to the space of p-integrable real-valued functions with respect to a positive and finite scalar measure.
The scope of the renovation project undertaken by McGowan Builders included the installation of a new Bar Beacon lounge in the 260-room luxury hotel, in addition to the installation of new corporate office and kitchen facility and function spaces in the lower level.
Local function spaces, heat and Navier-Stokes equations.
Homotopy theory of function spaces and related topics; proceedings.
The buyer is planning a complete modernization in keeping with the inn's Georgian architectural details, including a complete updating of the guest rooms and baths, corridors, lobby, meeting and function spaces and dining facilities, said J.
The fundamental difference between the two disciplines is that facility caterers must consider the availabilities and best uses of their function spaces, which may be limited.
Among the highlights are spectral, structural, and geometric properties of special types of operators on Banach spaces, emphasizing isometries, weighted composition operators, and projections on function spaces.
This first looks at function spaces based on intrinsic properties of a function, such as its size, continuity, smoothness, and various forms of control over the mean oscillation.
Among their topics are the Choquet theory of functional spaces, simplificial function spaces, topologies on boundaries, constructions of function spaces, and functional spaces in potential theory and the Dirichlet problem.
Oasis West Realty LLC has now formally commenced the entitlement process with the City of Beverly Hills to master develop and further improve the site, while respecting the existing hotel tower, the successful public areas, the function spaces of the hotel, as well as its important westerly gateway location in the City of Beverly Hills.