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https://math.stackexchange.com/questions/1542866/distribution-with-compact-support
Distribution with compact support. Ask Question Asked 4 years, 1 month ago. ... Support of a distribution, what does it mean? 3. Understanding why the domain of a distribution is defined to be smooth functions with compact support. 2. Continuous distribution-valued function induces distribution…
https://en.wikipedia.org/wiki/Distribution_(mathematics)
The basic space of test function consists of smooth functions with compact support, leading to standard distributions. Use of the space of smooth, rapidly (faster than any polynomial increases) decreasing test functions (these functions are called Schwartz functions ) gives instead the tempered distributions, which are important because they have a well-defined distributional Fourier transform.
https://www.sciencedirect.com/science/article/pii/S0079816908602779
This chapter discusses the Fourier transforms of distributions with compact support and Paley-Wiener theorem. This chapter considers a continuous function f with compact support in R n . The chapter mentions that the Fourier transform of a continuous function with compact support can be extended to the complex space C n , as an entire analytic function of exponential type.
https://link.springer.com/chapter/10.1007%2F978-0-8176-4675-2_8
Jul 21, 2010 · More generally, every distribution with compact support can be extended to a continuous linear form on \(C^\infty (X).\)Author: J. J. Duistermaat, J. A. C. Kolk
https://ncatlab.org/nlab/show/compactly+supported+distribution
A compactly supported distribution is a distribution whose support of a distribution is a compact subset. This implies that compactly supported distributions may be evaluated not just on bump functions, but in fact on the larger space of all smooth functions.
https://sites.math.washington.edu/~hart/m556/Lecture18.pdf
Distributions of Compact Support Hart Smith Department of Mathematics University of Washington, Seattle Math 526/556, Spring 2015
https://math.stackexchange.com/questions/1587781/support-of-a-distribution-what-does-it-mean
Basically, it means that there exist a compact set $K$ such that if a function has support only outside $K$, than the pairing of the function and the distribution is zero. It is more or less the dual notion of "compactly supported function".
https://www.mat.univie.ac.at/~stein/lehre/SoSem09/distrvo.pdf
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 describe distributions which have their support concentrated in a single point. 1.2.
http://www.math.chalmers.se/~hasse/distributioner_eng.pdf
When we shall extend di erential calculus to distributions, it is suitable to use in ntely di erentiable functions with compact support as test functions. In this chapter we will show that there is "a lot of" C 1 …
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