query: A funtion and its fourier transformation cannot both be compactly supported unless f=0
positive_passages.docid: 35982
positive_passages.text: A function and its Fourier transform cannot both be compactly supported
negative_passages.docid: 91257
negative_passages.text: Fourier basis functions
negative_passages.docid: 80735
negative_passages.text: Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
negative_passages.docid: 80588
negative_passages.text: The Fourier transform of a "comb function" is a comb function?
negative_passages.docid: 41946
negative_passages.text: Find the Fourier transform of the absolute value of a function, given its Fourier transform
negative_passages.docid: 107772
negative_passages.text: Separability of functions with compact support
negative_passages.docid: 105790
negative_passages.text: What is the Fourier Transform of $f'(x)/x$
negative_passages.docid: 110395
negative_passages.text: Integrable function $f$ on $\mathbb R$ does not imply that limit $f(x)$ is zero
negative_passages.docid: 99675
negative_passages.text: A closed ball in $l^{\infty}$ is not compact
negative_passages.docid: 5392
negative_passages.text: Compact support vs. vanishing at infinity?
negative_passages.docid: 124335
negative_passages.text: An identity for Fourier transform of measure
negative_passages.docid: 65876
negative_passages.text: A normed space of continuous functions with norm $\int_{0}^{1}|f(t)|dt$ is not complete
negative_passages.docid: 140972
negative_passages.text: Uniform convergence of harmonic functions to $0$ on compact subsets
negative_passages.docid: 87119
negative_passages.text: A positive "Fourier transform" is integrable
negative_passages.docid: 31319
negative_passages.text: An integrable and periodic function $f(x)$ satisfies $\int_{0}^{T}f(x)dx=\int_{a}^{a+T}f(x)dx$.
negative_passages.docid: 153271
negative_passages.text: Fourier transform is uniformly continuous
negative_passages.docid: 151796
negative_passages.text: There is not an holomorphic function on a bounded domain such that $\lim_{z \to w} f(z)= \infty$ for every $w \in Fr(\Omega)$