Weighted space

Weighted space

In functional analysis, a weighted space is a space of functions under a "weighted norm", which is a finite norm (or semi-norm) that involves multiplication by a particular function referred to as the "weight".

Weights can be used to expand or reduce a space of considered functions. For example, in the space of functions from a set Usubsetmathbb{R} to mathbb{R} under the norm |cdot|_U defined by:|f|_U=sup_{xin U} is finite for many fewer functions.

When the weight is of the form frac{1}{1+x^m}, the weighted space is called "polynomial-weighted". [cite journal|last=Walczak|first=Zbigniew|year=2005|title=On the rate of convergence for some linear operators|journal=Hiroshima Mathematical Journal|volume=35|pages=115–124|url=http://www.math.sci.hiroshima-u.ac.jp/hmj/v35.1/p115-124.pdf]

References


*cite encyclopedia|editor=Michiel Hazewinkel|year=2001|encyclopedia=Encyclopaedia of Mathematics|publisher=Springer|last=Kudryavtsev|first=L D|title=Weighted Space|url=http://eom.springer.de/W/w097580.htm


Wikimedia Foundation. 2010.

Игры ⚽ Поможем решить контрольную работу

Look at other dictionaries:

  • Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …   Wikipedia

  • Lp space — In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p norm for finite dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford Schwartz 1958, III.3),… …   Wikipedia

  • Cluster-weighted modeling — In statistics, cluster weighted modeling (CWM) is an algorithm based approach to non linear prediction of outputs (dependent variables) from inputs (independent variables) based on density estimation using a set of models (clusters) that are each …   Wikipedia

  • Momentum space — The momentum space or k space associated with a particle is a vector space in which every point {kx,ky,kz} corresponds to a possible value of the momentum vector . Representing a problem in terms of the momenta of the particles involved, rather… …   Wikipedia

  • Projective space — In mathematics a projective space is a set of elements constructed from a vector space such that a distinct element of the projective space consists of all non zero vectors which are equal up to a multiplication by a non zero scalar. A formal… …   Wikipedia

  • Inner product space — In mathematics, an inner product space is a vector space with the additional structure of inner product. This additional structure associates each pair of vectors in the space with a scalar quantity known as the inner product of the vectors.… …   Wikipedia

  • CIE 1931 color space — In the study of color perception, one of the first mathematically defined color spaces is the CIE 1931 XYZ color space, created by the International Commission on Illumination (CIE) in 1931.[1][2] The CIE XYZ color space was derived from a series …   Wikipedia

  • Monolith (Space Odyssey) — Chaos Computer Club used a model of the 2001 monolith at the Hackers at Large camp site Monoliths are fictional advanced machines built by an unseen extraterrestrial species that appear in Arthur C. Clarke s Space Odyssey series of novels and… …   Wikipedia

  • K-space (MRI) — independently introduced in 1983 by Ljunggren [Ljunggren S. Journal of Magnetic Resonance 1983; 54:338.] and Twieg [cite journal | author = Twieg D | title = The k trajectory formulation of the NMR imaging process with applications in analysis… …   Wikipedia

  • Ultrametric space — In mathematics, an ultrametric space is a special kind of metric space in which the triangle inequality is replaced with d(x, z) ≤ max{d(x, y), d(y, z)}. Sometimes the associated metric is also called a non Archimedean metric or super metric.… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”