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


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