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https://en.wikipedia.org/wiki/Distribution_(mathematics)
Distribution of compact support. It is also possible to define the convolution of two distributions S and T on R n, provided one of them has compact support. Informally, in order to define S∗T where T has compact support, the idea is to extend the definition of the convolution ∗ to a linear operation on distributions so that the ...
https://en.wikipedia.org/wiki/Support_(mathematics)
Compact support ... functions, via convolution. In good cases, functions with compact support are dense in the space of functions that vanish at infinity, ... In Fourier analysis in particular, it is interesting to study the singular support of a distribution.
https://math.stackexchange.com/questions/395100/what-will-be-the-support-of-the-convolution-of-two-test-functions
Remark 2: I don't know a expliclty characterization of the support of the convolution, but by the given formula, you can see that if the two functions has compact support, then does the convolution. Update: I have corrected some errors in the text.
https://www.mat.univie.ac.at/~stein/lehre/SoSem09/distrvo.pdf
Next we de ne the support of a distribution and introduce the localization of a distribu-tion to an open set. We invoke partitions of unity to show that a distribution is uniquely determined by its localizations. Finally we discuss distributions with compact support and identify them with continuous linear forms on C∞. Moreover, we completely ...
http://galton.uchicago.edu/~lalley/Courses/381/Convolutions-Smoothing.pdf
6 Convolution,Smoothing,andWeakConvergence ... on R with compact support then for any finite Borel measure µ the convolution g ... is the convolution of the distribution of Y mwith that of P n∏ +1Un/2 n. Since Y m has a density of classCm°2, Corollary 6.6 implies thatY has a density of classCm°2. But since
https://www.sciencedirect.com/science/article/pii/S0079816908618905
This chapter describes the convolution of a distribution with a testfunction. When the distribution T has compact support, the corresponding convolution mapping carries the space of testfunctions into itself.
https://rouxph.blogspot.com/2014/05/convolution-dune-distribution-par-une.html
Dans un premier billet sur la convolution des distributions j'ai expliqué comment on peut définir la convolution d'une distribution par une fonction test. Cette définition est assez contraignante car dans beaucoup d'applications on a besoin de pouvoir convoler des distributions avec la …
https://www.coursera.org/lecture/theorie-des-distributions/partie-2-convolution-des-distributions-XA1on
Eh bien cette formule vaut encore pour un produit de convolution de distribution et plus précisément, théorème: pour toute distribution T sur R N, pour toute distribution S à support compact sur R N, eh bien on a la formule, pour tout monôme différentiel d rond alpha, autrement dit pour tout multiindice à N composantes d rond alpha de T ...
http://www.math.chalmers.se/~hasse/distributioner_eng.pdf
The theory of distribution tries to remedy this by imbedding ... 8 Convolution of distributions 36 9 Fundamental solutions 43 ... use in ntely di erentiable functions with compact support as test functions. In this chapter we will show that there is "a lot of" C1 0-functions.
https://www.sciencedirect.com/science/article/pii/S0079816908618917
This chapter discusses the convolution of distributions. The chapter assumes T as a distribution on R n and S another distribution with compact support. The distribution S defines a mapping of the space of testfunctions into itself; this mapping is sequentially continuous and commutes with translation.
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