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https://math.stackexchange.com/questions/26628/infinitely-differentiable-function-with-compact-support
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https://www.encyclopediaofmath.org/index.php/Function_of_compact_support
can serve as an example of an infinitely-differentiable function of compact support in a domain containing the sphere .. The set of all infinitely-differentiable functions of compact support in a domain is denoted by .On one can define linear functionals (generalized functions, cf. Generalized function).With the aid of functions one can define generalized solutions (cf. Generalized solution ...
https://math.stackexchange.com/questions/1283783/an-example-of-an-infinitely-differentiable-function-with-compact-support
Could anyone give me a function infinitely differentiable on the real line and having a compact support? And the function must be nonnegative and normalized, i.e. the integration of the function on the real line must be one. I tried to think of one myself, but it seems trickier than expected.
https://ui.adsabs.harvard.edu/abs/2017arXiv170205442A/abstract
An infinitely differentiable function with compact support: Definition and properties Arias de Reyna, Juan; Abstract. This is the English translation of my old paper 'Definición y estudio de una función indefinidamente diferenciable de soporte compacto', Rev. Real Acad. Ciencias 76 (1982) 21-38. In it a function (essentially Fabius function ...Cited by: 1
https://www.sciencedirect.com/topics/mathematics/infinitely-differentiable-function
To obtain a relation that is widely applicable, a “weak” version of the partial derivative of a function is needed. For k ∈ N 0 ∪ {∞}, let K k = K R k (R n) denote the collection of all functions in C k (R n) with compact support, and let D = D (R n) denote the class of all infinitely differentiable functions on R n with compact support.
https://arxiv.org/abs/1702.05442
Title: An infinitely differentiable function with compact support: Definition and properties. Authors: Juan Arias de Reyna (Submitted on 17 Feb 2017) Abstract: This is the English translation of my old paper 'Definici\'on y estudio de una funci\'on indefinidamente diferenciable de soporte compacto', Rev. Real Acad. Ciencias 76 (1982) 21-38. In ...Cited by: 1
https://dlmf.nist.gov/1.16
The closure of the set of points where ϕ ≠ 0 is called the support of ϕ. If the support of ϕ is a compact set (§ 1.9(vii)), then ϕ is called a function of compact support. A test function is an infinitely differentiable function of compact support.
https://www.math.colostate.edu/~pauld/M545/6Distrib.pdf
if f x 0 for x in the complement of a compact subset of U. In particular, if U Rn, then f has compact support if there is a positive constant, C such that f x 0 for x C. We say that f x is a test function if f has compact support and, in addition, f is infinitely differentiable on U. We use the notation f Cc U or f D U to indicate that f is a ...
https://web.math.princeton.edu/~const/spa.pdf
0. The complement of the support of a distribution is naturally de ned as the largest open set where the distribution vanishes, and so it follows that spt(u) ˆK. Conversely, if u2D0(Rn) has compact support K, then it is easy to see that u(˚) = u(˚˜) where ˜is a C1 0 function identically equal to 1 …
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