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https://math.stackexchange.com/questions/26628/infinitely-differentiable-function-with-compact-support
Infinitely differentiable function with compact support. Ask Question Asked 8 years, ... (1-x^2)$ as a linear combination of $1/(1\pm x)$ to write $\phi$ as a product of two infinitely differentiable functions. share cite improve this answer. answered Mar 12 '11 at 23:47. Did Did. ... Twice differentiable functions with compact support. 0.
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://www.sciencedirect.com/topics/mathematics/infinitely-differentiable-function
If Ω is an open set in ℝ n, then an infinitely differentiable function φ: Ω → ℂ is in the set C 0 ∞ (Ω) if it has a compact support. The space D(Ω) is the set C 0 …
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://arxiv.org/abs/1702.05442
We gratefully acknowledge support from the Simons Foundation and member institutions. ... An infinitely differentiable function with compact support: Definition and ... (1982) 21-38. In it a function (essentially Fabius function) is defined and given its main properties, including: unicity, interpretation as a probability, partition of unity ...Cited by: 1
https://dlmf.nist.gov/1.16
A test function is an infinitely differentiable function of compact support. A sequence { ϕ n } of test functions converges to a test function ϕ if the support of every ϕ n is contained in a fixed compact set K and as n → ∞ the sequence { ϕ n ( k ) } converges uniformly on K to ϕ ( k ) for k = 0 , 1 , 2 , … .
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