Weierstrass transform
id:
weierstrass-transform-174-2943509
title:
Weierstrass transform
text:
In mathematics, the Weierstrass transform of a function f : R → R, named after Karl Weierstrass, is a "smoothed" version of f obtained by averaging the values of f, weighted with a Gaussian centered at x. Specifically, it is the function F defined by
- F = 1 4 π ∫ − ∞ ∞ f e − 2 4 d y = 1 4 π ∫ − ∞ ∞ f e − y 2 4 d y , the convolution of f with the Gaussian function
- 1 4 π e − x 2 / 4 . The factor 1 4 π is chosen so that the Gaussian will have a total integral of 1, with the consequence th
brand slug:
wiki
category slug:
encyclopedia
description:
"Smoothing" integral transform
original url:
https://en.wikipedia.org/wiki/Weierstrass_transform
date created:
2008-05-17T03:02:23Z
date modified:
2024-09-02T14:52:13Z
main entity:
{"identifier":"Q7979829","url":"https://www.wikidata.org/entity/Q7979829"}
image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/9/99/Weierstrass_transform.svg","width":720,"height":458}
fields total:
13
integrity:
16