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https://en.wikipedia.org/wiki/Distribution_(mathematics)
The distribution T has compact support if its support is a compact set. Explicitly, T has compact support if there is a compact subset K of U such that for every test function whose support is completely outside of K, we have T() = 0.
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://math.stackexchange.com/questions/1587781/support-of-a-distribution-what-does-it-mean
I find it hard to understand what support of a distribution really means. For example What does it mean for a distribution to have compact support? If an ordinary function has compact support I can visualize this as some sort of bump function. But how should I …
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 …
https://www.sciencedirect.com/science/article/pii/S0079816908618863
This chapter discusses the support of a distribution. If T is a distribution, the support of T is the set of all points x in such that for every neighborhood U of x there exists a test function, which is defined in the chapter. When the distribution is a continuous function, its support as a distribution function and its support as a continuous function is the same set.
https://mathoverflow.net/questions/348395/on-compact-support-distributions
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https://www.encyclopediaofmath.org/index.php/Function_of_compact_support
The support of is the closure of the set of points for which is different from zero . Thus one can also say that a function of compact support in is a function defined on such that its support is a closed bounded set located at a distance from the boundary of by a number greater than , where is sufficiently small.
http://www.math.chalmers.se/~hasse/distributioner_eng.pdf
The theory of distribution tries to remedy this by imbedding classical functions in a larger class of objects, the so called distributions (or ... 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. Notation Let
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 ...
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