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https://en.wikipedia.org/wiki/Smooth_function
A bump function is a smooth function with compact support. In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous. A smooth function is a function that has derivatives of all orders everywhere in its domain.
https://www.planetmath.org/SmoothFunctionsWithCompactSupport
Then the set of smooth functions with compact support (in U) is the set of functions f:ℝn→ℂ which are smooth (i.e., ∂αf:ℝn→ℂ is a continuous function for all multi-indices α) and suppf is compact and contained in U. This function space is denoted by C0∞(U).
https://math.stackexchange.com/questions/67370/smooth-functions-with-compact-support-are-dense-in-l1
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https://www.chebfun.org/examples/approx/SmoothCompact.html
Smooth functions of compact support Nick Trefethen, July 2014 in approx download ...
https://math.rice.edu/~semmes/fun5.pdf
Some basic aspects of smooth functions and distributions on open subsets of Rn are briefly discussed. Contents 1 Smooth functions 2 2 Supremum seminorms 3 3 Countably many seminorms 4 4 Cauchy sequences 5 5 Compact support 6 6 Inductive limits 8 7 Distributions 9 8 Differentiation of distributions 10 9 Multiplication by smooth functions 11
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 , …
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.
https://mathoverflow.net/questions/224940/spectrum-of-ring-of-smooth-functions-on-mathbbrn/224941
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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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