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Results tagged with fourier-analysis
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user 317800
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.
1
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Delta-distribution composed with a function from the Fourier representation
The point of this coda to the above answers is to document the fact that it is possible to address this topic in a perfectly rigorous and elementary fashion. Let me start with the remarks that there …
- 406
0
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Well-defined distribution and its singular support
This question has already been answered but here is some additional material which might be of interest. One can show the existence of this distribution and even give a rather explicit representation …
- 406
1
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Integral mean value property
This is a comment but will be too long for that. The equation given is a (very simple) example of a difference-differential equation (in fact, a difference equation but there are several related que …
- 406
3
votes
Fourier transform of periodic distributions
This is a comment rather than an answer but it will be too long. There is a confusion in your statement which I find rather irritating and which has not, as far as I can see, been addressed here. I …
- 406
1
vote
Fourier transform of a generalized function on the plane
Chanced on this and after much rumination I have decided to point out the following flaws in the postings.
Firstly, I assume that when you write $$\frac 1 {x+y^2+i0}$$ you mean a limit of the functio …
- 406