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Results tagged with fourier-analysis
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user 6651
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.
18
votes
1
answer
3k
views
Let a function f have all moments zero. What conditions force f to be identically zero?
Throughout, let $f$ be a Lebesgue measurable function (or continuous if you wish, but this is probably no easier). (Questions with distributions etc. are possible also but I want to keep things simple …
- 1,990
10
votes
When I can safely assume that a function is a Laplace transform of other function?
This kind of question is very interesting, and I too would like to know answers.
Sorry to self-publicise; I hope it's not regarded as impolite, but since I have also considered this exact kind of ques …
- 1,990
3
votes
If the fourier transformed of f is odd, is f odd?
Yes. Using tempered distributions it's immediately obvious, since $f = C \mathcal{F}^3 (\mathcal{F} f)$ for a constant $C$, and $\mathcal{F}$ maps odd distributions into odd distributions.
The missi …
- 1,990
2
votes
Accepted
Understanding the inverse Laplace transform of a function with essential singularities
After taking a quick look at the paper, I agree with Robert Israel.
Almost no detailed justification is given (perhaps not surprising for a Physics journal...), and it seems to be not so easy to justi …
- 1,990
2
votes
The maximum of a real trigonometric polynomial
Even in the special case where $f(x) \geq 0$ for all $x$, there can't be any simple answer involving the coefficients $(a_n)$, $(b_n)$. You're basically asking to estimate the $L^\infty$ norm of a tri …
- 1,990
2
votes
Fourier Series application for dissertation
Fourier series are useful (and sometimes essential) for solving/understanding many problems involving periodic functions on $\mathbb{R}$ or, equivalently, functions $f$ on $[a,b]$ such that $f(a)=f(b) …