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Results tagged with fourier-analysis
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user 17261
The representation of functions (or objects which are in some generalize the notion of function) as constant linear combinations of sines and cosines at integer multiples of a given frequency, as Fourier transforms or as Fourier integrals.
3
votes
Does there exist a continuous function of compact support with Fourier transform outside L^1?
Choose
$$f(x)=
\begin{cases}
\dfrac{\frac12 -x}{\log(x)},&0<x\leq1/2\\
0,&\text{otherwise}
\end{cases}$$
Then $$\operatorname*{Im} \int_{0}^{\infty} dk \ e^{-\varepsilon k}
\int_{-\infty}^{\infty} dx …
- 2,753
2
votes
Vanishing periodizations $\sum_{k \in \mathbb Z} f(t+ak)$ of a function $f$ for different va...
The answer is no.
Proof by induction :
Let $f_n \neq 0$ with compact support such that the periodizations of $a_1,...,a_n$ are zero.
Then there exists an integer $m$ such that the function $f_{n+1}(x) …
- 2,753