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Results tagged with fourier-analysis
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user 10820
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.
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inequality for an integrable real valued function with a compactly supported fourier transform
Let $f$ be an integrable function on $\mathbb{R}$ where support($\hat{f}$) $\subseteq$ [$-\gamma, \gamma$] for some $ 0 < \gamma < 1$
Prove that | $f(x) - f(0)$| $ \leq c \gamma$ |x| $\underset{ y …
CommunityBot
- 1
-1
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a complex borel measure, whose Fourier transform goes to zero
I think I got a good one:
clealy, it's enough to prove $\mu$(singleton) = 0.
Consider the function $f_{\epsilon}(x) = \frac{1}{\epsilon}$ if 0 < x < $\infty$ and 0 otherwise.
Notice that as $\epsilo …
- 133
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4
answers
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a complex borel measure, whose Fourier transform goes to zero
I have $\mu$ a complex borel measure on $\mathbb(R)$, whose Fourier transform goes to zero as $ \xi$ goes to $ \infty$. I need to prove that $ |\mu|$(singleton) = 0.
Should I approach $\mu$ by a seque …
- 133
5
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1
answer
3k
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least condition for the Fourier transform to be integrable
I want to prove that if $f \in C^{1}(\mathbb{R})$ is compactly supported then its Fourier transform is integrable.
I was able to prove the result for $f \in C^{2}(\mathbb{R})$ and compactly supported. …
CommunityBot
- 1
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Plessner's Theorem (1929)
Does anyone link me to a reference that proves the following theorem for Plessner:
Let $\mu$ be a bounded complex Borel measure on $\mathbb{R}$
$\mu$ is absolutely continuous to the Lebesgue measure …
- 251