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https://math.stackexchange.com/questions/526449/fourier-transform-of-a-function-of-compact-support
Fourier transform of a function of compact support. Ask Question Asked 6 years, 2 months ago. ... On functions with Fourier transform having compact support. 1. ... Fourier Transform on a compact support. 2. Fourier Transform of Exponentially Decaying Function Cannot Have Compact Support. 0.
https://mathoverflow.net/questions/29991/fourier-transforms-of-compactly-supported-functions
Then $\hat{f}$ should remain unchanged when convolved with the Fourier transform of $\chi$, but since $\hat{f}$ lives on the reals you would like to think that this convolution would partially fill up some open set connected to the boundary of the original support of $\hat{f}$ and thus enlarge the support of $\hat{f}$.
https://math.stackexchange.com/questions/154454/a-function-and-its-fourier-transform-cannot-both-be-compactly-supported
A funtion and its fourier transformation cannot both be compactly supported unless f=0 1 If a function is compactly supported, then its Fourier series converge?
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://en.wikipedia.org/wiki/Pontryagin_duality
In particular, the Fourier transform is an isometry from the complex-valued continuous functions of compact support on G to the -functions on ^ (using the -norm with respect to μ for functions on G and the -norm with respect to ν for functions on ^).
http://math.uchicago.edu/~may/REU2013/REUPapers/Hill.pdf
the basic properties of the Fourier transform and show that a function and its Fourier transform cannot both have compact support. From there we prove the Fourier inversion theorem and use this to prove the classical uncertainty principle which shows that the spread of a function and its Fourier transform are inversely proportional. Finally, we
https://en.wikipedia.org/wiki/Talk:Convergence_of_Fourier_series
The Fourier transform for jpegs and mp3s can be viewed strictly in the discrete context, in which case the convergence is moot (since the Fourier series is a finite sum.) The remaining comments do not pertain to the convergence of Fourier series. Loisel 14:06, 24 Mar 2005 (UTC)(Rated B-class, Mid-importance): WikiProject Mathematics
https://www.osti.gov/pages/biblio/1427516
Abstract. In this paper, we present a new algorithm for computing the convolution of two compactly supported functions. The algorithm approximates the functions to be convolved using Fourier extensions and then uses the fast Fourier transform to efficiently compute Fourier extension approximations to the pieces of the result.
https://ui.adsabs.harvard.edu/abs/1999PhDT........75N/abstract
This work is an attempt to infer information about the nature of the zeros of the Fourier transform of continuous functions of compact support from the nature of coefficients of their polynomial approximation. Although the main thrust of this work has been directed towards the real functions of compact support, some simple complex cases are also considered. The concept of completeness of a ...Author: Arjang Jaden Noushin
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