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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, 9 months ago. ... Twice differentiable functions with compact support. 0. ...
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://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://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://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://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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