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https://en.wikipedia.org/wiki/Bump_function
Examples. The function : → given by = { (− −), ∈ (−,),is an example of a bump function in one dimension. It is clear from the construction that this function has compact support, since a function of the real line has compact support if and only if it has bounded and closed support.
https://math.stackexchange.com/questions/67370/smooth-functions-with-compact-support-are-dense-in-l1
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https://en.wikipedia.org/wiki/Support_(mathematics)
In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero. If the domain of f is a topological space, the support of f is instead defined as the smallest closed set containing all points not mapped to zero. This concept is used very widely in mathematical analysis
https://www.encyclopediaofmath.org/index.php/Function_of_compact_support
The support of is the closure of the set of points for which is different from zero . Thus one can also say that a function of compact support in is a function defined on such that its support is a closed bounded set located at a distance from the boundary of by a number greater than , where is sufficiently small.
https://math.stackexchange.com/questions/549966/example-of-smooth-function-without-compact-support-on-open-real-interval
What is an explicit example of a smooth function on a real open interval that does not have compact support, i.e. for given $a,b \in \mathbb{R}$, a function (in ...
https://www.chebfun.org/examples/approx/SmoothCompact.html
How do you make a smooth function with compact support? Ben Green tells me his favorite method is as follows. Given $h>0$, consider a square wave of width $h$ and ...
https://ocw.mit.edu/courses/mathematics/18-101-analysis-ii-fall-2005/lecture-notes/lecture14.pdf
3.9 Support and Compact Support Now for some terminology. Let U be an open set in Rn, and let f : U → R be a continuous function. Definition 3.26. The support of fis supp f= x∈ U: f(x) = 0}. (3.164) For example, supp f Q = Q. Definition 3.27. Let f : U → R be a continuous function. The function f is compactly supported if supp fis ...
http://texas.math.ttu.edu/~gilliam/f06/m5340_f06/mollifiers_approx.pdf
Mollifiers and Approximation by Smooth Functions with Compact Support Let ρ∈ C∞(Rn) be a non-negative function with support in the unit ball in Rn.In particular we assume that ρ(x) ≥ 0 for x∈ Rn, ρ(x) = 0 for kxk >1, and Z Rn ρ(x)dx= 1.
http://staff.ustc.edu.cn/~wangzuoq/Courses/16F-Manifolds/Notes/Lec03.pdf
2 LECTURE 3: SMOOTH FUNCTIONS then f 3 is a smooth function on Rn, which vanishes for all jxj 2, and 1 for all jxj 1, and 0 f 3(x) 1 for all x. With the help of these Euclidean bump functions, we can show that on any smooth manifold, there exists many many \bump" functions:
https://mathoverflow.net/questions/237636/are-compactly-supported-continuous-functions-dense-in-the-continuous-functions-o
Continuous functions on $\mathbb R^d$ such that the support is a compact subset of $\overline{\Omega}$? For "nice" $\Omega$ this would be the space of continuous functions on $\Omega$ vanishing at the boundary. $\endgroup$ – Jochen Wengenroth Apr 29 '16 at 12:50
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